GCSE Maths: Metric units and time (Higher)
Part of the GCSE Maths units and compound measures chapter (Higher). Chapter overview · Foundation version of this lesson · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Metric units and time
Every measurement has two parts: a number and a unit. “5” on its own means nothing, but 5 centimetres or 5 kilograms means something you can picture. The metric system is used almost everywhere in the world. Its great advantage is that units are linked by 10, 100 and 1000, so changing between them just means moving the decimal point.
The prefixes tell you the size: kilo means 1000 (a kilometre is 1000 metres), centi means one hundredth (a centimetre is 1/100 of a metre) and milli means one thousandth (a millimetre is 1/1000 of a metre). The same prefixes work for grams and litres.
The facts to learn
| Measure | Units and links |
|---|---|
| Length | 1 km = 1000 m · 1 m = 100 cm · 1 cm = 10 mm · 1 m = 1000 mm |
| Mass | 1 tonne = 1000 kg · 1 kg = 1000 g · 1 g = 1000 mg |
| Capacity | 1 litre = 1000 ml · 1 litre = 100 cl · 1 cl = 10 ml |
| Time | 1 minute = 60 seconds · 1 hour = 60 minutes · 1 day = 24 hours · 1 week = 7 days |
Which way do I go: multiply or divide?
Think about how many you will need. A metre is a big unit and a centimetre is small, so one metre needs 100 of the little ones. So when you change from a big unit to a small unit the number gets bigger: multiply. When you change from a small unit to a big unit the number gets smaller: divide. Always ask yourself whether your answer should be bigger or smaller than the number you started with. If it is the wrong way round, you used the wrong operation.
Multiplying or dividing by 10, 100 or 1000 moves the digits. For example 3.2 × 100 = 320 (digits move two places left on the place-value grid) and 4500 ÷ 1000 = 4.5 (three places right). Some conversions need two steps, such as kilometres to centimetres: go km → m → cm, so 1 km = 1000 × 100 = 100 000 cm.
Key ideas
- Big unit to small unit: multiply (you get more of them).
- Small unit to big unit: divide (you get fewer of them).
- Know: 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm, 1 kg = 1000 g, 1 tonne = 1000 kg, 1 litre = 1000 ml.
- To compare measurements, first write them all in the same unit.
Key words. A unit is a standard size we measure in. Kilometres and metres measure the same kind of thing, but one is bigger than the other.
Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).
- Decide what should happen to the number: kilometres to metres. Kilometres are the bigger unit and metres are the smaller unit, so it takes more metres to make the same amount. We expect the number to get bigger.4.7 km → ? m
- Change kilometres to metres. Use the fact 1 km = 1000 m. Each kilometre is 1000 m, so you need 1000 times as many metres as kilometres. The metre is the smaller unit, so the number gets bigger: multiply by 1000.4.7 × 1000 = 4700 m
- Write the answer with its unit. Always finish by writing the new unit.4.7 km = 4700 m
Check. Convert back: 4700 m gives 4.7 km (4700 ÷ 1000 = 4.7). ✓
Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.
Key words. A unit is a standard size we measure in. Grams and kilograms measure the same kind of thing, but one is bigger than the other.
Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).
- Decide what should happen to the number: grams to kilograms. Grams are the smaller unit and kilograms are the bigger unit, so it takes fewer kilograms to make the same amount. We expect the number to get smaller.2350 g → ? kg
- Change grams to kilograms. Use the fact 1 kg = 1000 g. It takes 1000 grams to make one kilogram, so you need 1000 times fewer kilograms than grams. The kilogram is the bigger unit, so the number gets smaller: divide by 1000.2350 ÷ 1000 = 2.35 kg
- Write the answer with its unit. Always finish by writing the new unit.2350 g = 2.35 kg
Check. Convert back: 2.35 kg gives 2350 g (2.35 × 1000 = 2350). ✓
Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.
Method. Convert every measurement to the same unit, then compare the numbers.
- Pick one unit to compare in. We cannot compare 3 km with 250 m directly. Put every measurement in the same unit first.We will use m.
- Convert each one to m. Going to a smaller unit: multiply. Going to a bigger unit: divide.2.4 km: 2.4 × 1000 = 2400 m
2350 m is already in m
2410 m is already in m - Put the numbers in order. Now they are in the same unit, so we can order them (smallest first).2350, 2400, 2410
- Write the original measurements in that order. The question asks for the measurements as they were given.2350 m, 2.4 km, 2410 m
Check. Compare the biggest and the smallest again in the common unit: they are 2410 and 2350 m. ✓
Watch out. Do not order the numbers as they are written. 250 m looks bigger than 3 km because 250 is bigger than 3, but 3 km is 3000 m, which is much longer.
Key words. A unit is a standard size we measure in. Tonnes and grams measure the same kind of thing, but one is bigger than the other.
Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).
- Decide what should happen to the number: tonnes to grams. Tonnes are the bigger unit and grams are the smaller unit, so it takes more grams to make the same amount. We expect the number to get bigger.0.06 tonnes → ? g
- Change tonnes to kilograms. Use the fact 1 tonne = 1000 kg. Each tonne is 1000 kg, so you need 1000 times as many kilograms as tonnes. The kilogram is the smaller unit, so the number gets bigger: multiply by 1000.0.06 × 1000 = 60 kg
- Change kilograms to grams. Use the fact 1 kg = 1000 g. Each kilogram is 1000 g, so you need 1000 times as many grams as kilograms. The gram is the smaller unit, so the number gets bigger: multiply by 1000.60 × 1000 = 60,000 g
- Write the answer with its unit. We went one unit at a time so each step uses a fact you already know.0.06 tonnes = 60,000 g
Check. Convert back: 60,000 g gives 0.06 tonnes (60,000 ÷ 1,000,000 = 0.06). ✓
Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.
Method. 1 cm = 10 mm, so changing centimetres to millimetres (a smaller unit) means multiplying by 10. The same rule works when the length is an algebraic expression.
- Write down the fact. Centimetres are bigger than millimetres, so there will be more millimetres.1 cm = 10 mm
- Multiply the whole expression by 10. The whole length (3x + 2) must be multiplied, so use brackets.10 × (3x + 2)
- Expand the brackets. Multiply each term inside by 10.10 × 3x = 30x and 10 × 2 = 20
Answer: (30x + 20) mm
Check. Try x = 1: (3 + 2) = 5 cm = 50 mm, and 30 + 20 = 50. ✓
Watch out. Multiply the whole bracket, not just the first term: 10 × 3x + 2 would be wrong.
Watch out
Do not use 100 for everything. There are 100 cm in a metre but 1000 m in a kilometre and 1000 g in a kilogram. Check each fact carefully, and check your answer is the right size (a car cannot be 4.5 cm long, and a pencil cannot be 15 m).Exercise 16A Metric units of length, mass and capacity
Non-calculatorKey words. A unit is a standard size we measure in. Metres and centimetres measure the same kind of thing, but one is bigger than the other.
Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).
- Decide what should happen to the number: metres to centimetres. Metres are the bigger unit and centimetres are the smaller unit, so it takes more centimetres to make the same amount. We expect the number to get bigger.3 m → ? cm
- Change metres to centimetres. Use the fact 1 m = 100 cm. Each metre is 100 cm, so you need 100 times as many centimetres as metres. The centimetre is the smaller unit, so the number gets bigger: multiply by 100.3 × 100 = 300 cm
- Write the answer with its unit. Always finish by writing the new unit.3 m = 300 cm
Check. Convert back: 300 cm gives 3 m (300 ÷ 100 = 3). ✓
Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.
Key words. A unit is a standard size we measure in. Centimetres and metres measure the same kind of thing, but one is bigger than the other.
Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).
- Decide what should happen to the number: centimetres to metres. Centimetres are the smaller unit and metres are the bigger unit, so it takes fewer metres to make the same amount. We expect the number to get smaller.450 cm → ? m
- Change centimetres to metres. Use the fact 1 m = 100 cm. It takes 100 centimetres to make one metre, so you need 100 times fewer metres than centimetres. The metre is the bigger unit, so the number gets smaller: divide by 100.450 ÷ 100 = 4.5 m
- Write the answer with its unit. Always finish by writing the new unit.450 cm = 4.5 m
Check. Convert back: 4.5 m gives 450 cm (4.5 × 100 = 450). ✓
Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.
Key words. A unit is a standard size we measure in. Kilometres and metres measure the same kind of thing, but one is bigger than the other.
Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).
- Decide what should happen to the number: kilometres to metres. Kilometres are the bigger unit and metres are the smaller unit, so it takes more metres to make the same amount. We expect the number to get bigger.2.5 km → ? m
- Change kilometres to metres. Use the fact 1 km = 1000 m. Each kilometre is 1000 m, so you need 1000 times as many metres as kilometres. The metre is the smaller unit, so the number gets bigger: multiply by 1000.2.5 × 1000 = 2500 m
- Write the answer with its unit. Always finish by writing the new unit.2.5 km = 2500 m
Check. Convert back: 2500 m gives 2.5 km (2500 ÷ 1000 = 2.5). ✓
Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.
Key words. A unit is a standard size we measure in. Metres and kilometres measure the same kind of thing, but one is bigger than the other.
Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).
- Decide what should happen to the number: metres to kilometres. Metres are the smaller unit and kilometres are the bigger unit, so it takes fewer kilometres to make the same amount. We expect the number to get smaller.6000 m → ? km
- Change metres to kilometres. Use the fact 1 km = 1000 m. It takes 1000 metres to make one kilometre, so you need 1000 times fewer kilometres than metres. The kilometre is the bigger unit, so the number gets smaller: divide by 1000.6000 ÷ 1000 = 6 km
- Write the answer with its unit. Always finish by writing the new unit.6000 m = 6 km
Check. Convert back: 6 km gives 6000 m (6 × 1000 = 6000). ✓
Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.
Key words. A unit is a standard size we measure in. Centimetres and millimetres measure the same kind of thing, but one is bigger than the other.
Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).
- Decide what should happen to the number: centimetres to millimetres. Centimetres are the bigger unit and millimetres are the smaller unit, so it takes more millimetres to make the same amount. We expect the number to get bigger.8 cm → ? mm
- Change centimetres to millimetres. Use the fact 1 cm = 10 mm. Each centimetre is 10 mm, so you need 10 times as many millimetres as centimetres. The millimetre is the smaller unit, so the number gets bigger: multiply by 10.8 × 10 = 80 mm
- Write the answer with its unit. Always finish by writing the new unit.8 cm = 80 mm
Check. Convert back: 80 mm gives 8 cm (80 ÷ 10 = 8). ✓
Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.
Key words. A unit is a standard size we measure in. Millimetres and centimetres measure the same kind of thing, but one is bigger than the other.
Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).
- Decide what should happen to the number: millimetres to centimetres. Millimetres are the smaller unit and centimetres are the bigger unit, so it takes fewer centimetres to make the same amount. We expect the number to get smaller.35 mm → ? cm
- Change millimetres to centimetres. Use the fact 1 cm = 10 mm. It takes 10 millimetres to make one centimetre, so you need 10 times fewer centimetres than millimetres. The centimetre is the bigger unit, so the number gets smaller: divide by 10.35 ÷ 10 = 3.5 cm
- Write the answer with its unit. Always finish by writing the new unit.35 mm = 3.5 cm
Check. Convert back: 3.5 cm gives 35 mm (3.5 × 10 = 35). ✓
Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.
Key words. A unit is a standard size we measure in. Kilograms and grams measure the same kind of thing, but one is bigger than the other.
Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).
- Decide what should happen to the number: kilograms to grams. Kilograms are the bigger unit and grams are the smaller unit, so it takes more grams to make the same amount. We expect the number to get bigger.4 kg → ? g
- Change kilograms to grams. Use the fact 1 kg = 1000 g. Each kilogram is 1000 g, so you need 1000 times as many grams as kilograms. The gram is the smaller unit, so the number gets bigger: multiply by 1000.4 × 1000 = 4000 g
- Write the answer with its unit. Always finish by writing the new unit.4 kg = 4000 g
Check. Convert back: 4000 g gives 4 kg (4000 ÷ 1000 = 4). ✓
Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.
Key words. A unit is a standard size we measure in. Grams and kilograms measure the same kind of thing, but one is bigger than the other.
Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).
- Decide what should happen to the number: grams to kilograms. Grams are the smaller unit and kilograms are the bigger unit, so it takes fewer kilograms to make the same amount. We expect the number to get smaller.3500 g → ? kg
- Change grams to kilograms. Use the fact 1 kg = 1000 g. It takes 1000 grams to make one kilogram, so you need 1000 times fewer kilograms than grams. The kilogram is the bigger unit, so the number gets smaller: divide by 1000.3500 ÷ 1000 = 3.5 kg
- Write the answer with its unit. Always finish by writing the new unit.3500 g = 3.5 kg
Check. Convert back: 3.5 kg gives 3500 g (3.5 × 1000 = 3500). ✓
Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.
Key words. A unit is a standard size we measure in. Tonnes and kilograms measure the same kind of thing, but one is bigger than the other.
Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).
- Decide what should happen to the number: tonnes to kilograms. Tonnes are the bigger unit and kilograms are the smaller unit, so it takes more kilograms to make the same amount. We expect the number to get bigger.2 tonnes → ? kg
- Change tonnes to kilograms. Use the fact 1 tonne = 1000 kg. Each tonne is 1000 kg, so you need 1000 times as many kilograms as tonnes. The kilogram is the smaller unit, so the number gets bigger: multiply by 1000.2 × 1000 = 2000 kg
- Write the answer with its unit. Always finish by writing the new unit.2 tonnes = 2000 kg
Check. Convert back: 2000 kg gives 2 tonnes (2000 ÷ 1000 = 2). ✓
Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.
Key words. A unit is a standard size we measure in. Kilograms and tonnes measure the same kind of thing, but one is bigger than the other.
Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).
- Decide what should happen to the number: kilograms to tonnes. Kilograms are the smaller unit and tonnes are the bigger unit, so it takes fewer tonnes to make the same amount. We expect the number to get smaller.7500 kg → ? tonnes
- Change kilograms to tonnes. Use the fact 1 tonne = 1000 kg. It takes 1000 kilograms to make one tonne, so you need 1000 times fewer tonnes than kilograms. The tonne is the bigger unit, so the number gets smaller: divide by 1000.7500 ÷ 1000 = 7.5 tonnes
- Write the answer with its unit. Always finish by writing the new unit.7500 kg = 7.5 tonnes
Check. Convert back: 7.5 tonnes gives 7500 kg (7.5 × 1000 = 7500). ✓
Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.
Key words. A unit is a standard size we measure in. Kilograms and grams measure the same kind of thing, but one is bigger than the other.
Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).
- Decide what should happen to the number: kilograms to grams. Kilograms are the bigger unit and grams are the smaller unit, so it takes more grams to make the same amount. We expect the number to get bigger.0.6 kg → ? g
- Change kilograms to grams. Use the fact 1 kg = 1000 g. Each kilogram is 1000 g, so you need 1000 times as many grams as kilograms. The gram is the smaller unit, so the number gets bigger: multiply by 1000.0.6 × 1000 = 600 g
- Write the answer with its unit. Always finish by writing the new unit.0.6 kg = 600 g
Check. Convert back: 600 g gives 0.6 kg (600 ÷ 1000 = 0.6). ✓
Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.
Key words. A unit is a standard size we measure in. Grams and kilograms measure the same kind of thing, but one is bigger than the other.
Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).
- Decide what should happen to the number: grams to kilograms. Grams are the smaller unit and kilograms are the bigger unit, so it takes fewer kilograms to make the same amount. We expect the number to get smaller.450 g → ? kg
- Change grams to kilograms. Use the fact 1 kg = 1000 g. It takes 1000 grams to make one kilogram, so you need 1000 times fewer kilograms than grams. The kilogram is the bigger unit, so the number gets smaller: divide by 1000.450 ÷ 1000 = 0.45 kg
- Write the answer with its unit. Always finish by writing the new unit.450 g = 0.45 kg
Check. Convert back: 0.45 kg gives 450 g (0.45 × 1000 = 450). ✓
Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.
Key words. A unit is a standard size we measure in. Litres and millilitres measure the same kind of thing, but one is bigger than the other.
Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).
- Decide what should happen to the number: litres to millilitres. Litres are the bigger unit and millilitres are the smaller unit, so it takes more millilitres to make the same amount. We expect the number to get bigger.3 litres → ? ml
- Change litres to millilitres. Use the fact 1 litre = 1000 ml. Each litre is 1000 ml, so you need 1000 times as many millilitres as litres. The millilitre is the smaller unit, so the number gets bigger: multiply by 1000.3 × 1000 = 3000 ml
- Write the answer with its unit. Always finish by writing the new unit.3 litres = 3000 ml
Check. Convert back: 3000 ml gives 3 litres (3000 ÷ 1000 = 3). ✓
Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.
Key words. A unit is a standard size we measure in. Millilitres and litres measure the same kind of thing, but one is bigger than the other.
Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).
- Decide what should happen to the number: millilitres to litres. Millilitres are the smaller unit and litres are the bigger unit, so it takes fewer litres to make the same amount. We expect the number to get smaller.4500 ml → ? litres
- Change millilitres to litres. Use the fact 1 litre = 1000 ml. It takes 1000 millilitres to make one litre, so you need 1000 times fewer litres than millilitres. The litre is the bigger unit, so the number gets smaller: divide by 1000.4500 ÷ 1000 = 4.5 litres
- Write the answer with its unit. Always finish by writing the new unit.4500 ml = 4.5 litres
Check. Convert back: 4.5 litres gives 4500 ml (4.5 × 1000 = 4500). ✓
Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.
Key words. A unit is a standard size we measure in. Centilitres and litres measure the same kind of thing, but one is bigger than the other.
Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).
- Decide what should happen to the number: centilitres to litres. Centilitres are the smaller unit and litres are the bigger unit, so it takes fewer litres to make the same amount. We expect the number to get smaller.250 cl → ? litres
- Change centilitres to litres. Use the fact 1 litre = 100 cl. It takes 100 centilitres to make one litre, so you need 100 times fewer litres than centilitres. The litre is the bigger unit, so the number gets smaller: divide by 100.250 ÷ 100 = 2.5 litres
- Write the answer with its unit. Always finish by writing the new unit.250 cl = 2.5 litres
Check. Convert back: 2.5 litres gives 250 cl (2.5 × 100 = 250). ✓
Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.
Key words. A unit is a standard size we measure in. Litres and centilitres measure the same kind of thing, but one is bigger than the other.
Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).
- Decide what should happen to the number: litres to centilitres. Litres are the bigger unit and centilitres are the smaller unit, so it takes more centilitres to make the same amount. We expect the number to get bigger.1.5 litres → ? cl
- Change litres to centilitres. Use the fact 1 litre = 100 cl. Each litre is 100 cl, so you need 100 times as many centilitres as litres. The centilitre is the smaller unit, so the number gets bigger: multiply by 100.1.5 × 100 = 150 cl
- Write the answer with its unit. Always finish by writing the new unit.1.5 litres = 150 cl
Check. Convert back: 150 cl gives 1.5 litres (150 ÷ 100 = 1.5). ✓
Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.
Key words. A unit is a standard size we measure in. Centilitres and millilitres measure the same kind of thing, but one is bigger than the other.
Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).
- Decide what should happen to the number: centilitres to millilitres. Centilitres are the bigger unit and millilitres are the smaller unit, so it takes more millilitres to make the same amount. We expect the number to get bigger.8 cl → ? ml
- Change centilitres to millilitres. Use the fact 1 cl = 10 ml. Each centilitre is 10 ml, so you need 10 times as many millilitres as centilitres. The millilitre is the smaller unit, so the number gets bigger: multiply by 10.8 × 10 = 80 ml
- Write the answer with its unit. Always finish by writing the new unit.8 cl = 80 ml
Check. Convert back: 80 ml gives 8 cl (80 ÷ 10 = 8). ✓
Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.
Key words. A unit is a standard size we measure in. Millilitres and centilitres measure the same kind of thing, but one is bigger than the other.
Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).
- Decide what should happen to the number: millilitres to centilitres. Millilitres are the smaller unit and centilitres are the bigger unit, so it takes fewer centilitres to make the same amount. We expect the number to get smaller.90 ml → ? cl
- Change millilitres to centilitres. Use the fact 1 cl = 10 ml. It takes 10 millilitres to make one centilitre, so you need 10 times fewer centilitres than millilitres. The centilitre is the bigger unit, so the number gets smaller: divide by 10.90 ÷ 10 = 9 cl
- Write the answer with its unit. Always finish by writing the new unit.90 ml = 9 cl
Check. Convert back: 9 cl gives 90 ml (9 × 10 = 90). ✓
Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.
Method. Convert every measurement to the same unit, then compare the numbers.
- Pick one unit to compare in. We cannot compare 3 km with 250 m directly. Put every measurement in the same unit first.We will use g.
- Convert each one to g. Going to a smaller unit: multiply. Going to a bigger unit: divide.1.2 kg: 1.2 × 1000 = 1200 g
950 g is already in g
1.05 kg: 1.05 × 1000 = 1050 g
1100 g is already in g - Put the numbers in order. Now they are in the same unit, so we can order them (largest first).1200, 1100, 1050, 950
- Write the original measurements in that order. The question asks for the measurements as they were given.1.2 kg, 1100 g, 1.05 kg, 950 g
Check. Compare the biggest and the smallest again in the common unit: they are 950 and 1200 g. ✓
Watch out. Do not order the numbers as they are written. 250 m looks bigger than 3 km because 250 is bigger than 3, but 3 km is 3000 m, which is much longer.
Key words. A unit is a standard size we measure in. Kilometres and centimetres measure the same kind of thing, but one is bigger than the other.
Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).
- Decide what should happen to the number: kilometres to centimetres. Kilometres are the bigger unit and centimetres are the smaller unit, so it takes more centimetres to make the same amount. We expect the number to get bigger.0.4 km → ? cm
- Change kilometres to metres. Use the fact 1 km = 1000 m. Each kilometre is 1000 m, so you need 1000 times as many metres as kilometres. The metre is the smaller unit, so the number gets bigger: multiply by 1000.0.4 × 1000 = 400 m
- Change metres to centimetres. Use the fact 1 m = 100 cm. Each metre is 100 cm, so you need 100 times as many centimetres as metres. The centimetre is the smaller unit, so the number gets bigger: multiply by 100.400 × 100 = 40,000 cm
- Write the answer with its unit. We went one unit at a time so each step uses a fact you already know.0.4 km = 40,000 cm
Check. Convert back: 40,000 cm gives 0.4 km (40,000 ÷ 100,000 = 0.4). ✓
Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.
Key words. A unit is a standard size we measure in. Tonnes and grams measure the same kind of thing, but one is bigger than the other.
Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).
- Decide what should happen to the number: tonnes to grams. Tonnes are the bigger unit and grams are the smaller unit, so it takes more grams to make the same amount. We expect the number to get bigger.0.02 tonnes → ? g
- Change tonnes to kilograms. Use the fact 1 tonne = 1000 kg. Each tonne is 1000 kg, so you need 1000 times as many kilograms as tonnes. The kilogram is the smaller unit, so the number gets bigger: multiply by 1000.0.02 × 1000 = 20 kg
- Change kilograms to grams. Use the fact 1 kg = 1000 g. Each kilogram is 1000 g, so you need 1000 times as many grams as kilograms. The gram is the smaller unit, so the number gets bigger: multiply by 1000.20 × 1000 = 20,000 g
- Write the answer with its unit. We went one unit at a time so each step uses a fact you already know.0.02 tonnes = 20,000 g
Check. Convert back: 20,000 g gives 0.02 tonnes (20,000 ÷ 1,000,000 = 0.02). ✓
Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.
Key words. A unit is a standard size we measure in. Kilometres and millimetres measure the same kind of thing, but one is bigger than the other.
Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).
- Decide what should happen to the number: kilometres to millimetres. Kilometres are the bigger unit and millimetres are the smaller unit, so it takes more millimetres to make the same amount. We expect the number to get bigger.3 km → ? mm
- Change kilometres to metres. Use the fact 1 km = 1000 m. Each kilometre is 1000 m, so you need 1000 times as many metres as kilometres. The metre is the smaller unit, so the number gets bigger: multiply by 1000.3 × 1000 = 3000 m
- Change metres to centimetres. Use the fact 1 m = 100 cm. Each metre is 100 cm, so you need 100 times as many centimetres as metres. The centimetre is the smaller unit, so the number gets bigger: multiply by 100.3000 × 100 = 300,000 cm
- Change centimetres to millimetres. Use the fact 1 cm = 10 mm. Each centimetre is 10 mm, so you need 10 times as many millimetres as centimetres. The millimetre is the smaller unit, so the number gets bigger: multiply by 10.300,000 × 10 = 3,000,000 mm
- Write the answer with its unit. We went one unit at a time so each step uses a fact you already know.3 km = 3,000,000 mm
Check. Convert back: 3,000,000 mm gives 3 km (3,000,000 ÷ 1,000,000 = 3). ✓
Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.
Key words. A unit is a standard size we measure in. Milligrams and kilograms measure the same kind of thing, but one is bigger than the other.
Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).
- Decide what should happen to the number: milligrams to kilograms. Milligrams are the smaller unit and kilograms are the bigger unit, so it takes fewer kilograms to make the same amount. We expect the number to get smaller.5,000,000 mg → ? kg
- Change milligrams to grams. Use the fact 1 g = 1000 mg. It takes 1000 milligrams to make one gram, so you need 1000 times fewer grams than milligrams. The gram is the bigger unit, so the number gets smaller: divide by 1000.5,000,000 ÷ 1000 = 5000 g
- Change grams to kilograms. Use the fact 1 kg = 1000 g. It takes 1000 grams to make one kilogram, so you need 1000 times fewer kilograms than grams. The kilogram is the bigger unit, so the number gets smaller: divide by 1000.5000 ÷ 1000 = 5 kg
- Write the answer with its unit. We went one unit at a time so each step uses a fact you already know.5,000,000 mg = 5 kg
Check. Convert back: 5 kg gives 5,000,000 mg (5 × 1,000,000 = 5,000,000). ✓
Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.
Method. Put both amounts in the same unit, then see how many times one fits into the other.
- Change 1.5 kg to grams. 1 kg = 1000 g and kilograms to grams means multiply by 1000.1.5 × 1000 = 1500 g
- Divide by the portion size. The number of portions is how many 250 g fit into 1500 g.1500 ÷ 250 = 6
- Write the answer. 6 portions
Check. 6 × 250 = 1500 g = 1.5 kg. ✓
Watch out. Do not divide 1.5 by 250. The units must match before you divide.
Method. Change litres to millilitres so the units match, then divide.
- Change 1.2 litres to ml. Litres are bigger than ml, so multiply by 1000.1.2 × 1000 = 1200 ml
- Divide by the size of one glass. This counts how many 150 ml fit in 1200 ml.1200 ÷ 150 = 8
- Write the answer. 8 glasses
Check. 8 × 150 = 1200 ml = 1.2 litres. ✓
Method. Check the conversion fact, then redo the calculation.
- Write the correct fact. There are 1000 g in 1 kg, not 100 g.1 kg = 1000 g
- Redo the conversion. Kilograms to grams: multiply by 1000.3.5 × 1000 = 3500 g
- Explain the mistake. Sam multiplied by 100 (the cm-to-m fact) instead of 1000.Sam used 100 instead of 1000. Correct answer: 3500 g
Check. 350 g is only about one third of a kilogram, so it cannot be 3.5 kg. ✓
Watch out. Learn each fact separately: centi means 100, kilo means 1000.
Method. Find the total distance in metres, then change to kilometres.
- Multiply the lap length by the number of laps. 5 laps of 400 m each.400 × 5 = 2000 m
- Change metres to kilometres. Metres are smaller than kilometres, so divide by 1000.2000 ÷ 1000 = 2 km
- Write the answer. 2 km
Check. 2 km = 2000 m = 5 × 400 m. ✓
Method. Change every length to centimetres first, then add.
- Change 1.4 m to cm. Metres to centimetres: multiply by 100.1.4 × 100 = 140 cm
- Change 800 mm to cm. Millimetres to centimetres: divide by 10.800 ÷ 10 = 80 cm
- Add the three lengths. 35 cm is already in centimetres.140 + 35 + 80 = 255 cm
Check. In mm: 1400 + 350 + 800 = 2550 mm = 255 cm. ✓
Method. Write all three masses in kilograms, then add.
- Change 850 g to kg. Grams to kilograms: divide by 1000.850 ÷ 1000 = 0.85 kg
- Add the masses. Line up the decimal points.1.2 + 0.85 + 2.05 = 4.1 kg
Check. In grams: 1200 + 850 + 2050 = 4100 g = 4.1 kg. ✓
Method. Change metres to centimetres, divide, and use the remainder.
- Change 3 m to cm. Metres to centimetres: multiply by 100.3 × 100 = 300 cm
- Divide by the piece length. See how many whole 35 cm pieces fit.300 ÷ 35 = 8 remainder 20
- Write the answer. The remainder is the wood left over.8 pieces, 20 cm left over
Check. 8 × 35 + 20 = 280 + 20 = 300. ✓
Method. Change the bottle size to ml, then divide by the dose.
- Change litres to ml. Litres to ml: multiply by 1000.0.25 × 1000 = 250 ml
- Divide by the dose. How many 5 ml fit into 250 ml?250 ÷ 5 = 50
Check. 50 × 5 = 250 ml = 0.25 litres. ✓
Method. Change both lengths to metres and compare.
- Change 0.05 km to m. Kilometres to metres: multiply by 1000.0.05 × 1000 = 50 m
- Change 5000 cm to m. Centimetres to metres: divide by 100.5000 ÷ 100 = 50 m
- Compare. 50 m = 50 m, so neither is longer: they are equal.
Check. Both in cm: 0.05 km = 5000 cm. ✓
Method. Find the mass of one bag in grams, then multiply by the number of bags.
- Change 0.75 kg to grams. Kilograms to grams: multiply by 1000.0.75 × 1000 = 750 g
- Multiply by n. n bags weigh n times as much as one bag.750 × n = 750n
Check. Try n = 2: 2 × 0.75 = 1.5 kg = 1500 g, and 750 × 2 = 1500. ✓
Method. Find the perimeter in cm, change to metres, then simplify.
- Write the perimeter in centimetres. A square has four equal sides.4 × x = 4x cm
- Change to metres. Centimetres to metres: divide by 100.4x ÷ 100 = 4x100
- Simplify the fraction. Divide top and bottom by 4.4x100 = x25
Check. If x = 50, perimeter = 200 cm = 2 m and 50 ÷ 25 = 2. ✓
Method. Find how many drips happen in a day, then convert millilitres to litres.
- Find the number of seconds in a day. 1 day = 24 hours, 1 hour = 60 min, 1 min = 60 s.24 × 60 × 60 = 86400 seconds
- Find how many 10-second drips that is. Each drip takes 10 seconds.86400 ÷ 10 = 8640 drips
- Find the total water in ml. Each drip is 2 ml.8640 × 2 = 17280 ml
- Change to litres. Millilitres to litres: divide by 1000.17280 ÷ 1000 = 17.28 litres
Check. Per hour: 360 drips = 720 ml; per day 24 × 720 = 17 280 ml = 17.28 litres. ✓
Watch out. Work in one unit at a time and write the unit on every line.
Units of time
Time is the one common measure that is not metric. The facts are 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day and 7 days in a week. So changing between time units uses 60, 24 and 7 instead of 10, 100 and 1000. The same rule holds: to a smaller unit, multiply; to a bigger unit, divide. For example 2.5 hours is 2.5 × 60 = 150 minutes.
The 12-hour and 24-hour clock
The 12-hour clock uses am (morning, before midday) and pm (afternoon and evening). The 24-hour clock counts all the way from 00:00 (midnight) to 23:59, so there is no need for am or pm. After 12:59, add 12 to the hour: 3:20 pm is 15:20. To go back, subtract 12: 20:45 is 8:45 pm. Midnight is 00:00 (or 12 am) and midday is 12:00 (12 pm).
How long does it take? (durations)
Do not subtract 24-hour times like ordinary numbers, because an hour has 60 minutes, not 100. Instead count on: go from the start time to the next whole hour, then jump whole hours, then add the last few minutes. If the finish time is earlier than the start time, the journey goes past midnight into the next day.
Decimal hours
A calculator gives times as decimals, such as 2.4 hours. This does not mean 2 hours 40 minutes! The 0.4 is 0.4 of an hour, which is 0.4 × 60 = 24 minutes. To change hours and minutes into a decimal, divide the minutes by 60: 3 hours 15 minutes = 3 + 15/60 = 3.25 hours.
Key ideas
- 60 s = 1 min, 60 min = 1 hour, 24 hours = 1 day, 7 days = 1 week.
- After 12:59 add 12 to turn pm into 24-hour time; subtract 12 to go back.
- Find a time difference by counting on: to the next hour, then whole hours, then minutes.
- Decimal hours × 60 = minutes. Minutes ÷ 60 = decimal hours.
Key words. The 24-hour clock counts the hours from 00:00 to 23:59. 15:30 is 3:30 pm. Duration means how long something lasts.
Method. To find a time difference, count on from the start time to the finish time in easy jumps: to the next whole hour, then whole hours, then the minutes left.
- Write both times on the 24-hour clock. The 24-hour clock avoids am and pm mix-ups.Start 09:35, finish 13:20
- Count on to the next whole hour. Counting on in easy jumps is safer than subtracting 24-hour times, because there are 60 minutes (not 100) in an hour.09:35 to 10:00 = 25 minutes
- Count on in whole hours. Now we are at the start of an hour, so we can jump whole hours.10:00 to 13:00 = 3 hours
- Count on the remaining minutes. Finish by counting on to the finishing time.13:00 to 13:20 = 20 minutes
- Add the pieces together. The total is the time taken.25 minutes + 3 hours + 20 minutes = 3 hours 45 minutes
Check. Add back: 09:35 + 3 hours 45 minutes = 13:20. ✓
Watch out. Never subtract 24-hour times like 1420 − 0950 as ordinary numbers. An hour has 60 minutes, not 100.
Key words. The 24-hour clock counts the hours from 00:00 to 23:59. 15:30 is 3:30 pm. Duration means how long something lasts.
Method. To find a time difference, count on from the start time to the finish time in easy jumps: to the next whole hour, then whole hours, then the minutes left.
- Write both times on the 24-hour clock. The 24-hour clock avoids am and pm mix-ups.Start 22:45, finish 02:10 (the next day)
- Count on to the next whole hour. Counting on in easy jumps is safer than subtracting 24-hour times, because there are 60 minutes (not 100) in an hour.22:45 to 23:00 = 15 minutes
- Count on in whole hours. Now we are at the start of an hour, so we can jump whole hours.23:00 to 02:00 = 3 hours
- Count on the remaining minutes. Finish by counting on to the finishing time.02:00 to 02:10 = 10 minutes
- Add the pieces together. The total is the time taken.15 minutes + 3 hours + 10 minutes = 3 hours 25 minutes
Check. Add back: 22:45 + 3 hours 25 minutes = 02:10. ✓
Watch out. Never subtract 24-hour times like 1420 − 0950 as ordinary numbers. An hour has 60 minutes, not 100.
Method. Convert from the 12-hour clock to the 24-hour clock: add 12 to pm hours (except 12 pm); 12 am becomes 00.
- Decide: is it am or pm? am is before midday and pm is after midday. This decides whether we add 12.7:05 pm
- Add 12 to the hour (pm). The 24-hour clock carries on counting after 12 at midday: 1 pm is 13:00.7 + 12 = 19
- Write it with four digits. Always use two digits for the hour and two for the minutes.19:05
Check. 19:05 converted back is 7:05 pm. ✓
Method. Decimal hours are not hours and minutes. Keep the whole hours and multiply the decimal part by 60 to get minutes.
- Split off the whole hours. The digits before the decimal point are whole hours.2.4 hours = 2 hours + 0.4 hours
- Change the decimal part to minutes. There are 60 minutes in 1 hour, so multiply the decimal by 60.0.4 × 60 = 24 minutes
- Put them together. 2 hours 24 minutes
Check. 24 ÷ 60 = 0.4, so 2 hours 24 minutes is 2.4 hours. ✓
Watch out. 2.5 hours is not 2 hours 50 minutes. The .5 is half an hour = 30 minutes.
Watch out
Never write 2.4 hours as “2 hours 40 minutes”. The part after the decimal point is a fraction of an hour, not a number of minutes. Also, 100 minutes is not 1 hour; it is 1 hour 40 minutes.Exercise 16B Time
Non-calculatorKey words. A unit is a standard size we measure in. Minutes and seconds measure the same kind of thing, but one is bigger than the other.
Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).
- Decide what should happen to the number: minutes to seconds. Minutes are the bigger unit and seconds are the smaller unit, so it takes more seconds to make the same amount. We expect the number to get bigger.3 minutes → ? seconds
- Change minutes to seconds. Use the fact 1 minute = 60 seconds. Each minute is 60 seconds, so you need 60 times as many seconds as minutes. The second is the smaller unit, so the number gets bigger: multiply by 60.3 × 60 = 180 seconds
- Write the answer with its unit. Always finish by writing the new unit.3 minutes = 180 seconds
Check. Convert back: 180 seconds gives 3 minutes (180 ÷ 60 = 3). ✓
Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.
Key words. A unit is a standard size we measure in. Hours and minutes measure the same kind of thing, but one is bigger than the other.
Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).
- Decide what should happen to the number: hours to minutes. Hours are the bigger unit and minutes are the smaller unit, so it takes more minutes to make the same amount. We expect the number to get bigger.2 hours → ? minutes
- Change hours to minutes. Use the fact 1 hour = 60 minutes. Each hour is 60 minutes, so you need 60 times as many minutes as hours. The minute is the smaller unit, so the number gets bigger: multiply by 60.2 × 60 = 120 minutes
- Write the answer with its unit. Always finish by writing the new unit.2 hours = 120 minutes
Check. Convert back: 120 minutes gives 2 hours (120 ÷ 60 = 2). ✓
Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.
Key words. A unit is a standard size we measure in. Seconds and minutes measure the same kind of thing, but one is bigger than the other.
Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).
- Decide what should happen to the number: seconds to minutes. Seconds are the smaller unit and minutes are the bigger unit, so it takes fewer minutes to make the same amount. We expect the number to get smaller.180 seconds → ? minutes
- Change seconds to minutes. Use the fact 1 minute = 60 seconds. It takes 60 seconds to make one minute, so you need 60 times fewer minutes than seconds. The minute is the bigger unit, so the number gets smaller: divide by 60.180 ÷ 60 = 3 minutes
- Write the answer with its unit. Always finish by writing the new unit.180 seconds = 3 minutes
Check. Convert back: 3 minutes gives 180 seconds (3 × 60 = 180). ✓
Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.
Key words. A unit is a standard size we measure in. Minutes and hours measure the same kind of thing, but one is bigger than the other.
Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).
- Decide what should happen to the number: minutes to hours. Minutes are the smaller unit and hours are the bigger unit, so it takes fewer hours to make the same amount. We expect the number to get smaller.300 minutes → ? hours
- Change minutes to hours. Use the fact 1 hour = 60 minutes. It takes 60 minutes to make one hour, so you need 60 times fewer hours than minutes. The hour is the bigger unit, so the number gets smaller: divide by 60.300 ÷ 60 = 5 hours
- Write the answer with its unit. Always finish by writing the new unit.300 minutes = 5 hours
Check. Convert back: 5 hours gives 300 minutes (5 × 60 = 300). ✓
Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.
Key words. A unit is a standard size we measure in. Days and hours measure the same kind of thing, but one is bigger than the other.
Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).
- Decide what should happen to the number: days to hours. Days are the bigger unit and hours are the smaller unit, so it takes more hours to make the same amount. We expect the number to get bigger.5 days → ? hours
- Change days to hours. Use the fact 1 day = 24 hours. Each day is 24 hours, so you need 24 times as many hours as days. The hour is the smaller unit, so the number gets bigger: multiply by 24.5 × 24 = 120 hours
- Write the answer with its unit. Always finish by writing the new unit.5 days = 120 hours
Check. Convert back: 120 hours gives 5 days (120 ÷ 24 = 5). ✓
Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.
Key words. A unit is a standard size we measure in. Weeks and days measure the same kind of thing, but one is bigger than the other.
Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).
- Decide what should happen to the number: weeks to days. Weeks are the bigger unit and days are the smaller unit, so it takes more days to make the same amount. We expect the number to get bigger.3 weeks → ? days
- Change weeks to days. Use the fact 1 week = 7 days. Each week is 7 days, so you need 7 times as many days as weeks. The day is the smaller unit, so the number gets bigger: multiply by 7.3 × 7 = 21 days
- Write the answer with its unit. Always finish by writing the new unit.3 weeks = 21 days
Check. Convert back: 21 days gives 3 weeks (21 ÷ 7 = 3). ✓
Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.
Method. Convert from the 12-hour clock to the 24-hour clock: add 12 to pm hours (except 12 pm); 12 am becomes 00.
- Decide: is it am or pm? am is before midday and pm is after midday. This decides whether we add 12.7:30 am
- Keep the hour (am). Morning hours are the same on both clocks.The hour stays 7
- Write it with four digits. Always use two digits for the hour and two for the minutes.07:30
Check. 07:30 converted back is 7:30 am. ✓
Method. Convert from the 12-hour clock to the 24-hour clock: add 12 to pm hours (except 12 pm); 12 am becomes 00.
- Decide: is it am or pm? am is before midday and pm is after midday. This decides whether we add 12.2:15 pm
- Add 12 to the hour (pm). The 24-hour clock carries on counting after 12 at midday: 1 pm is 13:00.2 + 12 = 14
- Write it with four digits. Always use two digits for the hour and two for the minutes.14:15
Check. 14:15 converted back is 2:15 pm. ✓
Method. Convert from the 12-hour clock to the 24-hour clock: add 12 to pm hours (except 12 pm); 12 am becomes 00.
- Decide: is it am or pm? am is before midday and pm is after midday. This decides whether we add 12.11:40 pm
- Add 12 to the hour (pm). The 24-hour clock carries on counting after 12 at midday: 1 pm is 13:00.11 + 12 = 23
- Write it with four digits. Always use two digits for the hour and two for the minutes.23:40
Check. 23:40 converted back is 11:40 pm. ✓
Method. Convert from the 12-hour clock to the 24-hour clock: add 12 to pm hours (except 12 pm); 12 am becomes 00.
- Decide: is it am or pm? am is before midday and pm is after midday. This decides whether we add 12.12:05 am
- Keep the hour (am). Morning hours are the same on both clocks. The only change is that 12 am (midnight) becomes 00.12 am becomes 00
- Write it with four digits. Always use two digits for the hour and two for the minutes.00:05
Check. 00:05 converted back is 12:05 am. ✓
Method. Convert from the 12-hour clock to the 24-hour clock: add 12 to pm hours (except 12 pm); 12 am becomes 00.
- Decide: is it am or pm? am is before midday and pm is after midday. This decides whether we add 12.12:30 pm
- Keep the hour: 12 pm is midday. 12:00 to 12:59 pm are the same on both clocks.The hour stays 12
- Write it with four digits. Always use two digits for the hour and two for the minutes.12:30
Check. 12:30 converted back is 12:30 pm. ✓
Method. Convert from the 12-hour clock to the 24-hour clock: add 12 to pm hours (except 12 pm); 12 am becomes 00.
- Decide: is it am or pm? am is before midday and pm is after midday. This decides whether we add 12.9:05 pm
- Add 12 to the hour (pm). The 24-hour clock carries on counting after 12 at midday: 1 pm is 13:00.9 + 12 = 21
- Write it with four digits. Always use two digits for the hour and two for the minutes.21:05
Check. 21:05 converted back is 9:05 pm. ✓
Method. Convert from the 24-hour clock to the 12-hour clock: subtract 12 from hours bigger than 12 and write pm.
- Look at the hour. Before 12:00 the time is in the morning (am) and the hour stays the same.06:45
- Write it on the 12-hour clock. Add am.6:45 am
Check. Convert back: 6:45 am on a 24-hour clock is 06:45. ✓
Method. Convert from the 24-hour clock to the 12-hour clock: subtract 12 from hours bigger than 12 and write pm.
- Subtract 12 from the hour. After 12:59 the time is pm. This undoes the “add 12” rule.13 − 12 = 1
- Write it with pm. The minutes do not change.1:20 pm
Check. Convert back: 1:20 pm on a 24-hour clock is 13:20. ✓
Method. Convert from the 24-hour clock to the 12-hour clock: subtract 12 from hours bigger than 12 and write pm.
- Subtract 12 from the hour. After 12:59 the time is pm. This undoes the “add 12” rule.20 − 12 = 8
- Write it with pm. The minutes do not change.8:05 pm
Check. Convert back: 8:05 pm on a 24-hour clock is 20:05. ✓
Method. Convert from the 24-hour clock to the 12-hour clock: subtract 12 from hours bigger than 12 and write pm.
- Look at the hour. 00 hours means just after midnight.00:15
- Write it on the 12-hour clock. Midnight is called 12 am.12:15 am
Check. Convert back: 12:15 am on a 24-hour clock is 00:15. ✓
Method. Convert from the 24-hour clock to the 12-hour clock: subtract 12 from hours bigger than 12 and write pm.
- Look at the hour. 12:00 to 12:59 is just after midday (pm) and the hour stays 12.12:50
- Write it on the 12-hour clock. Add pm.12:50 pm
Check. Convert back: 12:50 pm on a 24-hour clock is 12:50. ✓
Method. Convert from the 24-hour clock to the 12-hour clock: subtract 12 from hours bigger than 12 and write pm.
- Subtract 12 from the hour. After 12:59 the time is pm. This undoes the “add 12” rule.23 − 12 = 11
- Write it with pm. The minutes do not change.11:59 pm
Check. Convert back: 11:59 pm on a 24-hour clock is 23:59. ✓
Key words. The 24-hour clock counts the hours from 00:00 to 23:59. 15:30 is 3:30 pm. Duration means how long something lasts.
Method. To find a time difference, count on from the start time to the finish time in easy jumps: to the next whole hour, then whole hours, then the minutes left.
- Write both times on the 24-hour clock. The 24-hour clock avoids am and pm mix-ups.Start 07:15, finish 09:40
- Count on to the next whole hour. Counting on in easy jumps is safer than subtracting 24-hour times, because there are 60 minutes (not 100) in an hour.07:15 to 08:00 = 45 minutes
- Count on in whole hours. Now we are at the start of an hour, so we can jump whole hours.08:00 to 09:00 = 1 hours
- Count on the remaining minutes. Finish by counting on to the finishing time.09:00 to 09:40 = 40 minutes
- Add the pieces together. The total is the time taken.45 minutes + 1 hour + 40 minutes = 2 hours 25 minutes
Check. Add back: 07:15 + 2 hours 25 minutes = 09:40. ✓
Watch out. Never subtract 24-hour times like 1420 − 0950 as ordinary numbers. An hour has 60 minutes, not 100.
Key words. The 24-hour clock counts the hours from 00:00 to 23:59. 15:30 is 3:30 pm. Duration means how long something lasts.
Method. To find a time difference, count on from the start time to the finish time in easy jumps: to the next whole hour, then whole hours, then the minutes left.
- Write both times on the 24-hour clock. The 24-hour clock avoids am and pm mix-ups.Start 10:50, finish 14:25
- Count on to the next whole hour. Counting on in easy jumps is safer than subtracting 24-hour times, because there are 60 minutes (not 100) in an hour.10:50 to 11:00 = 10 minutes
- Count on in whole hours. Now we are at the start of an hour, so we can jump whole hours.11:00 to 14:00 = 3 hours
- Count on the remaining minutes. Finish by counting on to the finishing time.14:00 to 14:25 = 25 minutes
- Add the pieces together. The total is the time taken.10 minutes + 3 hours + 25 minutes = 3 hours 35 minutes
Check. Add back: 10:50 + 3 hours 35 minutes = 14:25. ✓
Watch out. Never subtract 24-hour times like 1420 − 0950 as ordinary numbers. An hour has 60 minutes, not 100.
Key words. The 24-hour clock counts the hours from 00:00 to 23:59. 15:30 is 3:30 pm. Duration means how long something lasts.
Method. To find a time difference, count on from the start time to the finish time in easy jumps: to the next whole hour, then whole hours, then the minutes left.
- Write both times on the 24-hour clock. The 24-hour clock avoids am and pm mix-ups.Start 16:35, finish 20:10
- Count on to the next whole hour. Counting on in easy jumps is safer than subtracting 24-hour times, because there are 60 minutes (not 100) in an hour.16:35 to 17:00 = 25 minutes
- Count on in whole hours. Now we are at the start of an hour, so we can jump whole hours.17:00 to 20:00 = 3 hours
- Count on the remaining minutes. Finish by counting on to the finishing time.20:00 to 20:10 = 10 minutes
- Add the pieces together. The total is the time taken.25 minutes + 3 hours + 10 minutes = 3 hours 35 minutes
Check. Add back: 16:35 + 3 hours 35 minutes = 20:10. ✓
Watch out. Never subtract 24-hour times like 1420 − 0950 as ordinary numbers. An hour has 60 minutes, not 100.
Key words. The 24-hour clock counts the hours from 00:00 to 23:59. 15:30 is 3:30 pm. Duration means how long something lasts.
Method. To find a time difference, count on from the start time to the finish time in easy jumps: to the next whole hour, then whole hours, then the minutes left.
- Write both times on the 24-hour clock. The 24-hour clock avoids am and pm mix-ups.Start 22:20, finish 01:05 (the next day)
- Count on to the next whole hour. Counting on in easy jumps is safer than subtracting 24-hour times, because there are 60 minutes (not 100) in an hour.22:20 to 23:00 = 40 minutes
- Count on in whole hours. Now we are at the start of an hour, so we can jump whole hours.23:00 to 01:00 = 2 hours
- Count on the remaining minutes. Finish by counting on to the finishing time.01:00 to 01:05 = 5 minutes
- Add the pieces together. The total is the time taken.40 minutes + 2 hours + 5 minutes = 2 hours 45 minutes
Check. Add back: 22:20 + 2 hours 45 minutes = 01:05. ✓
Watch out. Never subtract 24-hour times like 1420 − 0950 as ordinary numbers. An hour has 60 minutes, not 100.
Method. Add the hours, then the minutes. Carry an hour when the minutes pass 60.
- Add the hours first. Whole hours do not change the minutes part of the time.08:30 + 2 hours = 10:30
- Add the minutes. If the minutes go past 60, carry 1 hour. Think "how many minutes to the next hour?"10:30 + 45 minutes = 11:15
- Write the answer. Give the time on the 24-hour clock.11:15
Check. Count back: 11:15 minus 2 hours 45 minutes = 08:30. ✓
Method. Add the hours, then the minutes. Carry an hour when the minutes pass 60.
- Add the hours first. Whole hours do not change the minutes part of the time.13:40 + 1 hour = 14:40
- Add the minutes. If the minutes go past 60, carry 1 hour. Think "how many minutes to the next hour?"14:40 + 35 minutes = 15:15
- Write the answer. Give the time on the 24-hour clock.15:15
Check. Count back: 15:15 minus 1 hour 35 minutes = 13:40. ✓
Method. Add the hours, then the minutes. Carry an hour when the minutes pass 60.
- Add the hours first. Whole hours do not change the minutes part of the time.18:20 + 3 hours = 21:20
- Add the minutes. If the minutes go past 60, carry 1 hour. Think "how many minutes to the next hour?"21:20 + 50 minutes = 22:10
- Write the answer. Give the time on the 24-hour clock.22:10
Check. Count back: 22:10 minus 3 hours 50 minutes = 18:20. ✓
Method. Add the hours, then the minutes. Carry an hour when the minutes pass 60.
- Add the hours first. Whole hours do not change the minutes part of the time.21:45 + 4 hours = 01:45
- Add the minutes. If the minutes go past 60, carry 1 hour. Think "how many minutes to the next hour?"01:45 + 30 minutes = 02:15
- Write the answer (it is the next day). The time has passed 24:00, so it is after midnight on the next day.02:15 the next day
Check. Count back: 02:15 minus 4 hours 30 minutes = 21:45. ✓
Method. Decimal hours are not hours and minutes. Keep the whole hours and multiply the decimal part by 60 to get minutes.
- Split off the whole hours. The digits before the decimal point are whole hours.3.5 hours = 3 hours + 0.5 hours
- Change the decimal part to minutes. There are 60 minutes in 1 hour, so multiply the decimal by 60.0.5 × 60 = 30 minutes
- Put them together. 3 hours 30 minutes
Check. 30 ÷ 60 = 0.5, so 3 hours 30 minutes is 3.5 hours. ✓
Watch out. 2.5 hours is not 2 hours 50 minutes. The .5 is half an hour = 30 minutes.
Method. Decimal hours are not hours and minutes. Keep the whole hours and multiply the decimal part by 60 to get minutes.
- Split off the whole hours. The digits before the decimal point are whole hours.1.25 hours = 1 hours + 0.25 hours
- Change the decimal part to minutes. There are 60 minutes in 1 hour, so multiply the decimal by 60.0.25 × 60 = 15 minutes
- Put them together. 1 hours 15 minutes
Check. 15 ÷ 60 = 0.25, so 1 hours 15 minutes is 1.25 hours. ✓
Watch out. 2.5 hours is not 2 hours 50 minutes. The .5 is half an hour = 30 minutes.
Method. Decimal hours are not hours and minutes. Keep the whole hours and multiply the decimal part by 60 to get minutes.
- Split off the whole hours. The digits before the decimal point are whole hours.2.4 hours = 2 hours + 0.4 hours
- Change the decimal part to minutes. There are 60 minutes in 1 hour, so multiply the decimal by 60.0.4 × 60 = 24 minutes
- Put them together. 2 hours 24 minutes
Check. 24 ÷ 60 = 0.4, so 2 hours 24 minutes is 2.4 hours. ✓
Watch out. 2.5 hours is not 2 hours 50 minutes. The .5 is half an hour = 30 minutes.
Method. Decimal hours are not hours and minutes. Keep the whole hours and multiply the decimal part by 60 to get minutes.
- Split off the whole hours. The digits before the decimal point are whole hours.0.75 hours = 0 hours + 0.75 hours
- Change the decimal part to minutes. There are 60 minutes in 1 hour, so multiply the decimal by 60.0.75 × 60 = 45 minutes
- Put them together. 0 hours 45 minutes
Check. 45 ÷ 60 = 0.75, so 0 hours 45 minutes is 0.75 hours. ✓
Watch out. 2.5 hours is not 2 hours 50 minutes. The .5 is half an hour = 30 minutes.
Method. To write hours and minutes as decimal hours, divide the minutes by 60 and add the whole hours.
- Change the minutes to a fraction of an hour. There are 60 minutes in 1 hour, so divide the minutes by 60.30 ÷ 60 = 0.5
- Add the whole hours. 2 + 0.5 = 2.5 hours
Check. 0.5 × 60 = 30 minutes. ✓
Watch out. Divide the minutes by 60, not by 100.
Method. To write hours and minutes as decimal hours, divide the minutes by 60 and add the whole hours.
- Change the minutes to a fraction of an hour. There are 60 minutes in 1 hour, so divide the minutes by 60.45 ÷ 60 = 0.75
- Add the whole hours. 1 + 0.75 = 1.75 hours
Check. 0.75 × 60 = 45 minutes. ✓
Watch out. Divide the minutes by 60, not by 100.
Method. To write hours and minutes as decimal hours, divide the minutes by 60 and add the whole hours.
- Change the minutes to a fraction of an hour. There are 60 minutes in 1 hour, so divide the minutes by 60.12 ÷ 60 = 0.2
- Add the whole hours. 3 + 0.2 = 3.2 hours
Check. 0.2 × 60 = 12 minutes. ✓
Watch out. Divide the minutes by 60, not by 100.
Method. To write hours and minutes as decimal hours, divide the minutes by 60 and add the whole hours.
- Change the minutes to a fraction of an hour. There are 60 minutes in 1 hour, so divide the minutes by 60.6 ÷ 60 = 0.1
- Add the whole hours. 4 + 0.1 = 4.1 hours
Check. 0.1 × 60 = 6 minutes. ✓
Watch out. Divide the minutes by 60, not by 100.
| Station | Time |
|---|---|
| Bellview | 07:48 |
| Corton | 08:26 |
| Dunmere | 09:05 |
| Eastgate | 09:41 |
Key words. The 24-hour clock counts the hours from 00:00 to 23:59. 15:30 is 3:30 pm. Duration means how long something lasts.
Method. To find a time difference, count on from the start time to the finish time in easy jumps: to the next whole hour, then whole hours, then the minutes left.
- Write both times on the 24-hour clock. The 24-hour clock avoids am and pm mix-ups.Start 07:48, finish 09:41
- Count on to the next whole hour. Counting on in easy jumps is safer than subtracting 24-hour times, because there are 60 minutes (not 100) in an hour.07:48 to 08:00 = 12 minutes
- Count on in whole hours. Now we are at the start of an hour, so we can jump whole hours.08:00 to 09:00 = 1 hours
- Count on the remaining minutes. Finish by counting on to the finishing time.09:00 to 09:41 = 41 minutes
- Add the pieces together. The total is the time taken.12 minutes + 1 hour + 41 minutes = 1 hour 53 minutes
Check. Add back: 07:48 + 1 hour 53 minutes = 09:41. ✓
Watch out. Never subtract 24-hour times like 1420 − 0950 as ordinary numbers. An hour has 60 minutes, not 100.
Key words. The 24-hour clock counts the hours from 00:00 to 23:59. 15:30 is 3:30 pm. Duration means how long something lasts.
Method. To find a time difference, count on from the start time to the finish time in easy jumps: to the next whole hour, then whole hours, then the minutes left.
- Write both times on the 24-hour clock. The 24-hour clock avoids am and pm mix-ups.Start 08:26, finish 09:05
- Count on to the next whole hour. Counting on in easy jumps is safer than subtracting 24-hour times, because there are 60 minutes (not 100) in an hour.08:26 to 09:00 = 34 minutes
- Count on the remaining minutes. Finish by counting on to the finishing time.09:00 to 09:05 = 5 minutes
- Add the pieces together. The total is the time taken.34 minutes + 5 minutes = 39 minutes
Check. Add back: 08:26 + 39 minutes = 09:05. ✓
Watch out. Never subtract 24-hour times like 1420 − 0950 as ordinary numbers. An hour has 60 minutes, not 100.
Method. Use the count-on method twice.
- Bellview to Corton. Count on from 07:48 to 08:00 (12 min), then to 08:26 (26 min).12 + 26 = 38 minutes
- Corton to Eastgate. Count on from 08:26 to 09:00 (34 min), then to 09:41 (41 min).34 + 41 = 75 minutes = 1 hour 15 minutes
Check. 38 + 75 = 113 minutes = 1 hour 53 minutes, the same as Bellview to Eastgate (07:48 to 09:41). ✓
Method. Change to the 24-hour clock, add the length of the film, then change back.
- Write the start on the 24-hour clock. pm times: add 12 to the hour.7:45 pm = 19:45
- Add the 2 hours. Whole hours first.19:45 + 2 hours = 21:45
- Add the 25 minutes. 21:45 + 15 minutes = 22:00, and 10 more minutes = 22:10.21:45 + 25 min = 22:10
- Change back to the 12-hour clock. Subtract 12 from the hours.22:10 = 10:10 pm
Check. Count back from 10:10 pm: minus 25 min = 9:45 pm, minus 2 h = 7:45 pm. ✓
Key words. A unit is a standard size we measure in. Days and seconds measure the same kind of thing, but one is bigger than the other.
Method. To change units, use the fact that links them. Changing to a smaller unit means a bigger number (multiply); changing to a bigger unit means a smaller number (divide).
- Decide what should happen to the number: days to seconds. Days are the bigger unit and seconds are the smaller unit, so it takes more seconds to make the same amount. We expect the number to get bigger.1 days → ? seconds
- Change days to hours. Use the fact 1 day = 24 hours. Each day is 24 hours, so you need 24 times as many hours as days. The hour is the smaller unit, so the number gets bigger: multiply by 24.1 × 24 = 24 hours
- Change hours to minutes. Use the fact 1 hour = 60 minutes. Each hour is 60 minutes, so you need 60 times as many minutes as hours. The minute is the smaller unit, so the number gets bigger: multiply by 60.24 × 60 = 1440 minutes
- Change minutes to seconds. Use the fact 1 minute = 60 seconds. Each minute is 60 seconds, so you need 60 times as many seconds as minutes. The second is the smaller unit, so the number gets bigger: multiply by 60.1440 × 60 = 86,400 seconds
- Write the answer with its unit. We went one unit at a time so each step uses a fact you already know.1 day = 86,400 seconds
Check. Convert back: 86,400 seconds gives 1 days (86,400 ÷ 86,400 = 1). ✓
Watch out. Ask yourself: will the number get bigger or smaller? Metres to centimetres: you get more of the smaller unit, so the number grows.
Method. Find the total minutes, then change to hours.
- Minutes in one week. 3 sessions of 50 minutes.3 × 50 = 150 minutes
- Minutes in 4 weeks. 4 weeks, 150 minutes each.150 × 4 = 600 minutes
- Change to hours. Minutes to hours: divide by 60.600 ÷ 60 = 10 hours
Check. 10 hours = 600 minutes, and 600 ÷ 4 ÷ 3 = 50. ✓
Method. Decimal hours are not hours and minutes. Keep the whole hours and multiply the decimal part by 60 to get minutes.
- Split off the whole hours. The digits before the decimal point are whole hours.3.4 hours = 3 hours + 0.4 hours
- Change the decimal part to minutes. There are 60 minutes in 1 hour, so multiply the decimal by 60.0.4 × 60 = 24 minutes
- Put them together. 3 hours 24 minutes
Check. 24 ÷ 60 = 0.4, so 3 hours 24 minutes is 3.4 hours. ✓
Watch out. 2.5 hours is not 2 hours 50 minutes. The .5 is half an hour = 30 minutes.
Method. Find the length of the shift, take off the break, then multiply by the hourly rate.
- Count on from 21:45 to 06:20. 21:45 to 22:00 is 15 minutes; 22:00 to 06:00 is 8 hours; 06:00 to 06:20 is 20 minutes.15 min + 8 h + 20 min = 8 hours 35 minutes
- Take off the unpaid break. Only time actually worked is paid.8 hours 35 minutes − 35 minutes = 8 hours
- Multiply by the rate of pay. Pay = rate × hours.£9.40 × 8 = £75.20
Check. Rough check: £10 × 8 = £80, a little more than £75.20. ✓
Method. Change hours and minutes to seconds separately, then add.
- Hours to seconds. 1 hour = 60 × 60 = 3600 seconds, so multiply t by 3600.t hours = 3600t seconds
- Minutes to seconds. 1 minute = 60 seconds.m minutes = 60m seconds
- Add. The total time is the two parts together.3600t + 60m seconds
Check. t = 1, m = 2: 1 hour 2 minutes = 3720 seconds and 3600 + 120 = 3720. ✓
Method. Find the total length of the concert, then subtract the interval.
- Count on from 7:30 pm to 10:05 pm. 7:30 to 10:00 is 2 hours 30 minutes, then 5 more minutes.2 h 30 min + 5 min = 2 hours 35 minutes
- Change to minutes. 2 hours = 120 minutes.120 + 35 = 155 minutes
- Subtract the interval. The music is not played during the interval.155 − 20 = 135 minutes
Check. 135 + 20 = 155 minutes = 2 h 35 min. ✓