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Primary Maths · Year 4Chapter 7 · Length, mass, capacity, perimeter and area
Year 4 · Perimeter, Area and Measures · Lesson 7.3

Year 4: Changing units: km, m, cm, mm, kg, g, l and ml

Part of the Year 4 perimeter, area and measures chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)

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7.3

Changing units: km, m, cm, mm, kg, g, l and ml

Year 4
Convert between units of measure, Decimals of measures, Kilometres, metres, centimetres, millimetres, Kilograms and grams, litres and millilitres

We use different units for different sizes. A kilometre (km) is for long distances. A metre (m) is for the size of a room. A centimetre (cm) and a millimetre (mm) are for small things. For mass we use kilograms (kg) and grams (g). For capacity we use litres (l) and millilitres (ml).

kmkilometremmetrecmcentimetremmmillimetre× 1000÷ 1000× 100÷ 100× 10÷ 10
Going right (to a smaller unit) we multiply. Going left (to a bigger unit) we divide.
LengthMassCapacity
10 mm = 1 cm1,000 g = 1 kg1,000 ml = 1 l
100 cm = 1 m
1,000 m = 1 km

Kilo means 1,000. Centi means one hundredth. Milli means one thousandth. These words help you remember the facts.

Big unit to small unit: multiply. A cm is small, so you need lots of cm to make 3 m. 3 m = 3 × 100 = 300 cm. The number gets bigger. Small unit to big unit: divide. It takes only a few big units to make the same length. 600 cm = 600 ÷ 100 = 6 m. The number gets smaller.

kgkilogramggram× 1000÷ 1000llitremlmillilitre× 1000÷ 1000
The same idea for mass (kg and g) and capacity (l and ml): multiply by 1,000 or divide by 1,000.

Decimals of measures. Half of a metre is 50 cm, and half is 0.5, so 0.5 m = 50 cm. For 2.5 m, change 2 m and 0.5 m separately: 200 cm + 50 cm = 250 cm. A double number line shows both units at once.

000.55011001.515022002.52503300mcm
2.5 m is the same distance as 250 cm. Each whole metre is 100 cm.

More decimals: 1.5 kg = 1,500 g. 0.25 l = 250 ml (a quarter of 1,000). 0.75 l = 750 ml. 4.5 km = 4,500 m. And going the other way, 1,500 g = 1.5 kg and 250 cm = 2.5 m.

Mixed units. 3 m 40 cm means 3 m and 40 cm. To write it in cm, change the 3 m to 300 cm and add 40 cm: 340 cm. And 1,450 ml is 1 l and 450 ml.

Key words. To convert is to change from one unit to another. The unit is the name we give a measure (cm, kg, ml...). A decimal uses a point, like 2.5.

Key ideas

  • 10 mm = 1 cm   100 cm = 1 m   1,000 m = 1 km   1,000 g = 1 kg   1,000 ml = 1 l.
  • Big unit to small unit: multiply (the number gets bigger).
  • Small unit to big unit: divide (the number gets smaller).
  • Halves and quarters: 0.5 = half, 0.25 = a quarter, 0.75 = three quarters.
  • 2.5 m = 250 cm and 1.5 kg = 1,500 g.
  • Mixed units: 3 m 40 cm = 300 cm + 40 cm = 340 cm.
Worked example 7.3.1
Change 3 m to centimetres.

Key words. To convert is to change a measure from one unit to another unit. Kilo means 1000: 1 kilometre = 1000 m, 1 kilogram = 1000 g. Centi means a hundredth: 1 m = 100 cm. Milli means a thousandth.

Method. There are 100 centimetres in 1 metre, so multiply by 100 to change metres to centimetres.

  1. Remember the fact. 1 m is the same as 100 cm. A centimetre is a much smaller unit, so we will have a bigger number.
    1 m = 100 cm
  2. Multiply by 100. Each m is 100 cm. So 3 m is 3 lots of 100 cm. (Multiplying by 100 moves every digit 2 places to the left.)
    3 × 100 = 300
  3. Write the answer with its unit. A measure always needs its unit.
    3 m = 300 cm

Check. Go back: 300 ÷ 100 = 3. ✓

Watch out. Changing to a smaller unit gives a bigger number: 3 m is 300 cm, not 0.03.

Worked example 7.3.2
Change 5 kg to grams.

Key words. To convert is to change a measure from one unit to another unit. Kilo means 1000: 1 kilometre = 1000 m, 1 kilogram = 1000 g. Centi means a hundredth: 1 m = 100 cm. Milli means a thousandth.

Method. There are 1,000 grams in 1 kilogram, so multiply by 1,000 to change kilograms to grams.

  1. Remember the fact. 1 kg is the same as 1,000 g. A gram is a much smaller unit, so we will have a bigger number.
    1 kg = 1,000 g
  2. Multiply by 1,000. Each kg is 1,000 g. So 5 kg is 5 lots of 1,000 g. (Multiplying by 1,000 moves every digit 3 places to the left.)
    5 × 1,000 = 5,000
  3. Write the answer with its unit. A measure always needs its unit.
    5 kg = 5,000 g

Check. Go back: 5,000 ÷ 1,000 = 5. ✓

Watch out. Changing to a smaller unit gives a bigger number: 5 kg is 5,000 g, not 0.005.

Worked example 7.3.3
A bottle holds 4 litres. How many millilitres is that?

Key words. To convert is to change a measure from one unit to another unit. Kilo means 1000: 1 kilometre = 1000 m, 1 kilogram = 1000 g. Centi means a hundredth: 1 m = 100 cm. Milli means a thousandth.

Method. There are 1,000 millilitres in 1 litre, so multiply by 1,000 to change litres to millilitres.

  1. Remember the fact. 1 l is the same as 1,000 ml. A millilitre is a much smaller unit, so we will have a bigger number.
    1 l = 1,000 ml
  2. Multiply by 1,000. Each l is 1,000 ml. So 4 l is 4 lots of 1,000 ml. (Multiplying by 1,000 moves every digit 3 places to the left.)
    4 × 1,000 = 4,000
  3. Write the answer with its unit. A measure always needs its unit.
    4 l = 4,000 ml

Check. Go back: 4,000 ÷ 1,000 = 4. ✓

Watch out. Changing to a smaller unit gives a bigger number: 4 l is 4,000 ml, not 0.004.

Worked example 7.3.4
Change 600 cm to metres.

Key words. To convert is to change a measure from one unit to another unit. Kilo means 1000: 1 kilometre = 1000 m, 1 kilogram = 1000 g. Centi means a hundredth: 1 m = 100 cm. Milli means a thousandth.

Method. There are 100 centimetres in 1 metre, so divide by 100 to change centimetres to metres.

  1. Remember the fact. 1 m is the same as 100 cm. A metre is a much bigger unit, so we will have a smaller number.
    100 cm = 1 m
  2. Divide by 100. Every 100 cm make 1 m. We find how many lots of 100 there are.
    600 ÷ 100 = 6
  3. Write the answer with its unit. A measure always needs its unit.
    600 cm = 6 m

Check. Go back: 6 × 100 = 600. ✓

Watch out. Changing to a bigger unit gives a smaller number. 600 cm is 6 m, not 60,000.

Worked example 7.3.5
A box has a mass of 7,000 g. What is its mass in kilograms?

Key words. To convert is to change a measure from one unit to another unit. Kilo means 1000: 1 kilometre = 1000 m, 1 kilogram = 1000 g. Centi means a hundredth: 1 m = 100 cm. Milli means a thousandth.

Method. There are 1,000 grams in 1 kilogram, so divide by 1,000 to change grams to kilograms.

  1. Remember the fact. 1 kg is the same as 1,000 g. A kilogram is a much bigger unit, so we will have a smaller number.
    1,000 g = 1 kg
  2. Divide by 1,000. Every 1,000 g make 1 kg. We find how many lots of 1,000 there are.
    7,000 ÷ 1,000 = 7
  3. Write the answer with its unit. A measure always needs its unit.
    7,000 g = 7 kg

Check. Go back: 7 × 1,000 = 7,000. ✓

Watch out. Changing to a bigger unit gives a smaller number. 7,000 g is 7 kg, not 7,000,000.

Worked example 7.3.6
Change 2.5 m to centimetres.
000.55011001.515022002.5?3300mcm

Key words. To convert is to change a measure from one unit to another unit. Kilo means 1000: 1 kilometre = 1000 m, 1 kilogram = 1000 g. Centi means a hundredth: 1 m = 100 cm. Milli means a thousandth.

Method. There are 100 centimetres in 1 metre, so multiply by 100 to change metres to centimetres.

  1. Remember the fact. 1 m is the same as 100 cm. A centimetre is a much smaller unit, so we will have a bigger number.
    1 m = 100 cm
  2. Split the number into whole metres and a part. It is easier to change the whole metres and the part separately.
    2.5 m = 2 m + 0.5 m
  3. Change the whole metres. Multiply by 100.
    2 × 100 = 200 cm
  4. Change the part. Think about what fraction of a m it is.
    0.5 m is half of 1 m. Half of 100 = 50 cm
  5. Add the two answers together.
    200 + 50 = 250 cm

Check. Go back: 250 ÷ 100 = 2.5. ✓

Watch out. Changing to a smaller unit gives a bigger number: 2.5 m is 250 cm, not 0.025.

Worked example 7.3.7
Change 1.5 kg to grams.

Key words. To convert is to change a measure from one unit to another unit. Kilo means 1000: 1 kilometre = 1000 m, 1 kilogram = 1000 g. Centi means a hundredth: 1 m = 100 cm. Milli means a thousandth.

Method. There are 1,000 grams in 1 kilogram, so multiply by 1,000 to change kilograms to grams.

  1. Remember the fact. 1 kg is the same as 1,000 g. A gram is a much smaller unit, so we will have a bigger number.
    1 kg = 1,000 g
  2. Split the number into whole kilograms and a part. It is easier to change the whole kilograms and the part separately.
    1.5 kg = 1 kg + 0.5 kg
  3. Change the whole kilograms. Multiply by 1,000.
    1 × 1,000 = 1,000 g
  4. Change the part. Think about what fraction of a kg it is.
    0.5 kg is half of 1 kg. Half of 1,000 = 500 g
  5. Add the two answers together.
    1,000 + 500 = 1,500 g

Check. Go back: 1,500 ÷ 1,000 = 1.5. ✓

Watch out. Changing to a smaller unit gives a bigger number: 1.5 kg is 1,500 g, not 0.0015.

Worked example 7.3.8
A path is 2,500 m long. Write its length in kilometres.

Key words. To convert is to change a measure from one unit to another unit. Kilo means 1000: 1 kilometre = 1000 m, 1 kilogram = 1000 g. Centi means a hundredth: 1 m = 100 cm. Milli means a thousandth.

Method. There are 1,000 metres in 1 kilometre, so divide by 1,000 to change metres to kilometres.

  1. Remember the fact. 1 km is the same as 1,000 m. A kilometre is a much bigger unit, so we will have a smaller number.
    1,000 m = 1 km
  2. Divide by 1,000 and keep the remainder. The whole kilometres come from the lots of 1,000 m. The remainder is the part left over.
    2,500 ÷ 1,000 = 2 remainder 500
  3. Write the remainder as a part of 1 km. 500 m out of 1,000 m is 500/1,000 of a km.
    500 m is half of 1,000 m, so 500 m = 0.5 km
  4. Put the whole kilometres and the part together. The whole number goes before the decimal point.
    2 + 0.5 = 2.5 km

Check. Go back: 2.5 × 1,000 = 2,500. ✓

Watch out. Changing to a bigger unit gives a smaller number. 2,500 m is 2.5 km, not 2,500,000.

Worked example 7.3.9
How many millilitres is 0.75 litres?

Key words. To convert is to change a measure from one unit to another unit. Kilo means 1000: 1 kilometre = 1000 m, 1 kilogram = 1000 g. Centi means a hundredth: 1 m = 100 cm. Milli means a thousandth.

Method. There are 1,000 millilitres in 1 litre, so multiply by 1,000 to change litres to millilitres.

  1. Remember the fact. 1 l is the same as 1,000 ml. A millilitre is a much smaller unit, so we will have a bigger number.
    1 l = 1,000 ml
  2. Split the number into whole litres and a part. It is easier to change the whole litres and the part separately.
    0.75 l is just a part of 1 l.
  3. Change the part. Think about what fraction of a l it is.
    0.75 l is three quarters of 1 l. 1,000 ÷ 4 = 250, then 250 × 3 = 750 ml
    So 0.75 l = 750 ml

Check. Go back: 750 ÷ 1,000 = 0.75. ✓

Watch out. Changing to a smaller unit gives a bigger number: 0.75 l is 750 ml, not 0.00075.

Worked example 7.3.10
Change 45 mm to centimetres.

Key words. To convert is to change a measure from one unit to another unit. Kilo means 1000: 1 kilometre = 1000 m, 1 kilogram = 1000 g. Centi means a hundredth: 1 m = 100 cm. Milli means a thousandth.

Method. There are 10 millimetres in 1 centimetre, so divide by 10 to change millimetres to centimetres.

  1. Remember the fact. 1 cm is the same as 10 mm. A centimetre is a much bigger unit, so we will have a smaller number.
    10 mm = 1 cm
  2. Divide by 10 and keep the remainder. The whole centimetres come from the lots of 10 mm. The remainder is the part left over.
    45 ÷ 10 = 4 remainder 5
  3. Write the remainder as a part of 1 cm. 5 mm out of 10 mm is 5/10 of a cm.
    5 mm is half of 10 mm, so 5 mm = 0.5 cm
  4. Put the whole centimetres and the part together. The whole number goes before the decimal point.
    4 + 0.5 = 4.5 cm

Check. Go back: 4.5 × 10 = 45. ✓

Watch out. Changing to a bigger unit gives a smaller number. 45 mm is 4.5 cm, not 450.

Worked example 7.3.11
Write 3 m 40 cm in centimetres.

Key words. To convert is to change a measure from one unit to another unit. Kilo means 1000: 1 kilometre = 1000 m, 1 kilogram = 1000 g. Centi means a hundredth: 1 m = 100 cm. Milli means a thousandth.

Method. Change the metres to centimetres, then add the centimetres that are left over.

  1. Change the whole metres to cm. 1 m = 100 cm, so multiply by 100.
    3 × 100 = 300 cm
  2. Add the extra cm. Put the two parts together.
    300 + 40 = 340 cm
  3. Write the answer. Use the small unit only.
    3 m 40 cm = 340 cm

Check. 340 ÷ 100 = 3 remainder 40. ✓

Watch out. Change the metres first. 3 m is 300 cm, not 3 cm. Then add the 40 cm.

Worked example 7.3.12
Write 1,450 ml in litres and millilitres.

Key words. To convert is to change a measure from one unit to another unit. Kilo means 1000: 1 kilometre = 1000 m, 1 kilogram = 1000 g. Centi means a hundredth: 1 m = 100 cm. Milli means a thousandth.

Method. Divide by 1,000 to find the whole litres. The remainder is the millilitres that are left over.

  1. Divide by 1,000. Every 1,000 ml make 1 l.
    1,450 ÷ 1,000 = 1 remainder 450
  2. Say what the answer means. The whole number is the litres. The remainder is the millilitres left over.
    1 l and 450 ml
  3. Write the answer. Put the big unit first, then the small unit.
    1,450 ml = 1 l 450 ml

Check. 1 × 1,000 + 450 = 1,450. ✓

Watch out. The remainder is not a decimal. It is the part left over, written in the smaller unit.

Watch out

Multiply or divide? Ask yourself: am I going to a smaller unit (more of them: multiply) or a bigger unit (fewer of them: divide)? Check the answer makes sense: 3 m is 300 cm, not 0.03 cm. And 3 m 40 cm is 340 cm, not 3.40 cm and not 34 cm.

Exercise 7D  Changing units

Non-calculator
1
FQuick-fire! Change each length to centimetres.
(a)4 m = ? cm
(b)9 m = ? cm
(c)12 m = ? cm
(d)30 m = ? cm
2
FFill in the missing number.
(a)3 kg = ? g
(b)8 kg = ? g
(c)5 l = ? ml
(d)12 l = ? ml
(e)6 km = ? m
(f)20 km = ? m
3
FChange each length to millimetres.
(a)5 cm = ? mm
(b)18 cm = ? mm
(c)40 cm = ? mm
4
FDivide to change to the bigger unit.
(a)700 cm = ? m
(b)4,000 g = ? kg
(c)9,000 ml = ? l
(d)5,000 m = ? km
(e)600 cm = ? m
(f)90 mm = ? cm
5
FThese measures have decimals. Change each one to the smaller unit.
(a)1.5 km = ? m
(b)2.5 kg = ? g
(c)0.5 l = ? ml
(d)3.5 m = ? cm
(e)0.25 l = ? ml
(f)1.75 m = ? cm
6
FChange each measure to the bigger unit. Your answers will have decimals.
(a)250 cm = ? m
(b)1,500 g = ? kg
(c)750 ml = ? l
(d)4,500 m = ? km
(e)35 mm = ? cm
(f)125 cm = ? m
7
FWrite each measure using only the smaller unit.
(a)3 m 40 cm = ? cm
(b)2 kg 350 g = ? g
(c)5 l 200 ml = ? ml
(d)1 km 750 m = ? m
8
FWrite each measure using two units (for example 1,450 g = 1 kg 450 g).
(a)275 cm = ?
(b)1,450 g = ?
(c)3,600 ml = ?
(d)2,300 m = ?
9
FUse the double number lines to fill in the missing numbers.
(a)
000.55011001.5?2200mcm
1.5 m = ? cm
(b)
000.5500110001.51500220002.5?33000kmm
2.5 km = ? m
10
PSA bridge is 2.4 km long. How long is the bridge in metres?
11
PSDev has a ribbon 3.5 m long. He cuts it into pieces that are each 50 cm long. How many pieces does he get?
12
PSA recipe needs 1.5 kg of flour. Mei has 900 g of flour. How much more flour does she need? Give your answer in grams.
13
RMei says, “3.5 km = 350 m.” What mistake has she made? What is the correct answer?
14
RAlways, sometimes or never true?   “When you change a length from metres to centimetres, the number gets bigger.” Explain.
15
RWhich is the odd one out?   2.5 m    250 cm    25 m    2 m 50 cm   Explain.
16
RI am a length. I am between 2 m and 3 m. In centimetres, my hundreds digit is 2, my tens digit is 5 and my ones digit is 0. What am I in centimetres? What am I in metres?

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