Year 5: Converting metric units
Part of the Year 5 units, perimeter, area, volume and time chapter. Chapter overview · whole chapter on one page
Converting metric units
A unit is the size we measure with. Metric units go up in tens, so each unit is a fixed number of the smaller unit below it:
| Measure | Units | Rule |
|---|---|---|
| Length | km and m | 1 km = 1,000 m |
| Length | m and cm | 1 m = 100 cm |
| Length | cm and mm | 1 cm = 10 mm |
| Mass | kg and g | 1 kg = 1,000 g |
| Capacity | litres and ml | 1 litre = 1,000 ml |
To change to a smaller unit, multiply. There are more small units, so the number gets bigger. To change to a bigger unit, divide. The number gets smaller. The decimal point moves in the same way: multiplying by 1,000 moves it three places to the right.
So 8.5 cm is the same as 85 mm. Five millimetres is half of one centimetre, so 0.5 cm = 5 mm.
Key ideas
- To change to a smaller unit, multiply. To change to a bigger unit, divide.
- Learn the rules: 1 km = 1,000 m, 1 m = 100 cm, 1 cm = 10 mm, 1 kg = 1,000 g, 1 litre = 1,000 ml.
- Check the size of your answer. 3.75 m must be less than 4 m, so 375 cm is the right size.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 km = 1,000 m
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.2.35 × 1,000 = 2,350
- Write the answer with the new unit. 2,350 m
Check. 2,350 ÷ 1,000 = 2.35, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.100 cm = 1 m
- Divide, because the new unit is bigger. A bigger unit fits in fewer times, so the number gets smaller.375 ÷ 100 = 3.75
- Write the answer with the new unit. 3.75 m
Check. 3.75 × 100 = 375, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1,000 ml = 1 litre
- Divide, because the new unit is bigger. A bigger unit fits in fewer times, so the number gets smaller.6,040 ÷ 1,000 = 6.04
- Write the answer with the new unit. 6.04 litres
Check. 6.04 × 1,000 = 6,040, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Watch out
A common mistake is to think that 1 cm = 100 mm. It is 10 mm, so 4.7 cm is 47 mm, not 470 mm. Also, 1 km is 1,000 m, not 100 m.Exercise 8A Changing between metric units
Non-calculatorKey words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 km = 1,000 m
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.2.4 × 1,000 = 2,400
- Write the answer with the new unit. 2,400 m
Check. 2,400 ÷ 1,000 = 2.4, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 km = 1,000 m
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.0.85 × 1,000 = 850
- Write the answer with the new unit. 850 m
Check. 850 ÷ 1,000 = 0.85, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 km = 1,000 m
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.1.06 × 1,000 = 1,060
- Write the answer with the new unit. 1,060 m
Check. 1,060 ÷ 1,000 = 1.06, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 km = 1,000 m
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.7.5 × 1,000 = 7,500
- Write the answer with the new unit. 7,500 m
Check. 7,500 ÷ 1,000 = 7.5, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 m = 100 cm
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.3.6 × 100 = 360
- Write the answer with the new unit. 360 cm
Check. 360 ÷ 100 = 3.6, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 m = 100 cm
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.0.45 × 100 = 45
- Write the answer with the new unit. 45 cm
Check. 45 ÷ 100 = 0.45, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 m = 100 cm
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.12.8 × 100 = 1,280
- Write the answer with the new unit. 1,280 cm
Check. 1,280 ÷ 100 = 12.8, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 cm = 10 mm
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.4.7 × 10 = 47
- Write the answer with the new unit. 47 mm
Check. 47 ÷ 10 = 4.7, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 cm = 10 mm
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.0.9 × 10 = 9
- Write the answer with the new unit. 9 mm
Check. 9 ÷ 10 = 0.9, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 cm = 10 mm
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.12.35 × 10 = 123.5
- Write the answer with the new unit. 123.5 mm
Check. 123.5 ÷ 10 = 12.35, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 kg = 1,000 g
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.2.5 × 1,000 = 2,500
- Write the answer with the new unit. 2,500 g
Check. 2,500 ÷ 1,000 = 2.5, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 kg = 1,000 g
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.0.35 × 1,000 = 350
- Write the answer with the new unit. 350 g
Check. 350 ÷ 1,000 = 0.35, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 kg = 1,000 g
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.4.08 × 1,000 = 4,080
- Write the answer with the new unit. 4,080 g
Check. 4,080 ÷ 1,000 = 4.08, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1,000 g = 1 kg
- Divide, because the new unit is bigger. A bigger unit fits in fewer times, so the number gets smaller.4,500 ÷ 1,000 = 4.5
- Write the answer with the new unit. 4.5 kg
Check. 4.5 × 1,000 = 4,500, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1,000 g = 1 kg
- Divide, because the new unit is bigger. A bigger unit fits in fewer times, so the number gets smaller.750 ÷ 1,000 = 0.75
- Write the answer with the new unit. 0.75 kg
Check. 0.75 × 1,000 = 750, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1,000 g = 1 kg
- Divide, because the new unit is bigger. A bigger unit fits in fewer times, so the number gets smaller.2,080 ÷ 1,000 = 2.08
- Write the answer with the new unit. 2.08 kg
Check. 2.08 × 1,000 = 2,080, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1,000 ml = 1 litre
- Divide, because the new unit is bigger. A bigger unit fits in fewer times, so the number gets smaller.2,500 ÷ 1,000 = 2.5
- Write the answer with the new unit. 2.5 litres
Check. 2.5 × 1,000 = 2,500, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1,000 ml = 1 litre
- Divide, because the new unit is bigger. A bigger unit fits in fewer times, so the number gets smaller.450 ÷ 1,000 = 0.45
- Write the answer with the new unit. 0.45 litres
Check. 0.45 × 1,000 = 450, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1,000 ml = 1 litre
- Divide, because the new unit is bigger. A bigger unit fits in fewer times, so the number gets smaller.1,875 ÷ 1,000 = 1.875
- Write the answer with the new unit. 1.875 litres
Check. 1.875 × 1,000 = 1,875, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 litre = 1,000 ml
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.1.2 × 1,000 = 1,200
- Write the answer with the new unit. 1,200 ml
Check. 1,200 ÷ 1,000 = 1.2, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 litre = 1,000 ml
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.0.7 × 1,000 = 700
- Write the answer with the new unit. 700 ml
Check. 700 ÷ 1,000 = 0.7, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 litre = 1,000 ml
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.3.05 × 1,000 = 3,050
- Write the answer with the new unit. 3,050 ml
Check. 3,050 ÷ 1,000 = 3.05, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Change both lengths to metres, then compare them.
- Change 2.5 km to metres. There are 1,000 m in 1 km.2.5 km = 2.5 × 1,000 = 2,500 m
- Compare the two lengths in metres. Both lengths are now in the same unit.2,500 m > 2,400 m
- Write the answer. 2.5 km is longer.
Check. 2.5 km is 2,500 m, which is 100 m more than 2,400 m. ✓
Watch out. Compare in the same unit. 2.5 looks smaller than 2,400, but 2.5 is in kilometres.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Change every measure to the same unit first. Then the numbers can be compared.
- Change every length to mm. Then all the numbers use the same unit, so we can compare them.0.8 m = 800 mm
85 cm = 850 mm
0.9 m = 900 mm
790 mm = 790 mm - Put the numbers in order, smallest first. The smallest number is the shortest length.790 < 800 < 850 < 900
- Write the answer with the original units. Write each length as it was given in the question.790 mm, 0.8 m, 85 cm, 0.9 m
Check. Read the list back: each length is < the next one. ✓
Watch out. Do not compare 790 with 0.8 as if they were in the same unit. Change them first.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Change the rope to centimetres, then count how many 40 cm pieces fit.
- Change 3.6 m to centimetres. There are 100 cm in 1 m.3.6 m = 3.6 × 100 = 360 cm
- Share the rope into 40 cm pieces. Count how many 40s fit into 360. Divide.360 ÷ 40 = 9
- Write the answer. The rope is shared exactly, with nothing left over.9 pieces
Check. 9 pieces × 40 cm = 360 cm. ✓
Watch out. Change the units first. Dividing 3.6 by 40 gives a wrong answer.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Change the litres to millilitres, then divide by the size of one cup.
- Change 1.5 litres to millilitres. There are 1,000 ml in 1 litre.1.5 litres = 1.5 × 1,000 = 1,500 ml
- Count how many 250 ml cups fit. Divide the total by the amount in each cup.1,500 ÷ 250 = 6
- Write the answer. 6 cups
Check. 6 × 250 ml = 1,500 ml. ✓
Watch out. Make sure both amounts are in millilitres before you divide.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Change the metre length to centimetres, then compare.
- Change 0.6 m to centimetres. There are 100 cm in 1 m.0.6 m = 0.6 × 100 = 60 cm
- Compare with 65 cm. Both lengths are now in centimetres.60 cm < 65 cm
- Write the answer. No. 0.6 m is 60 cm, which is shorter than 65 cm.
Check. Jo compared the digits 6 and 5, but the place values are different. ✓
Watch out. Comparing 0.6 with 65 as if they were the same unit gives the wrong answer.