Convert compound measurements

One amount can have two names

A route is 2 km 350 m long. Each kilometre contains 1000 metres. The distance is 2000 + 350 = 2350 m.

A bottle holds 1 ℓ 250 ml. Each litre contains 1000 millilitres, so it holds 1000 + 250 = 1250 ml.

km measures length in kilometres; ml measures liquid volume in millilitres. A unit is part of the meaning of your number.

Convert each part, then join

For 3 kg 40 g, three kilograms make 3000 g. Add 40 g to get 3040 g. The zero in 40 does not turn 40 g into 400 g.

For 4 m 8 cm, four metres make 400 cm. Add 8 cm: 408 cm.

To reverse the process, split 2075 ml into two groups of 1000 ml and 75 ml left. The amount is 2 ℓ 75 ml.

Take out every complete litre before writing the millilitres left over. Both parts matter: 2 ℓ alone loses 75 ml, while 2 ℓ 750 ml is too much. Although 1 ℓ 1075 ml names the same amount, another complete litre can be exchanged; 2 ℓ 75 ml has fewer than 1000 ml in its smaller part. Use fewer than 100 cm when the larger unit is metres; the other pairs in the table use 1000.

Check your understanding 1 Write the matching measurement

Write 5 m 6 cm in centimetres only.

Length in cm

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506 cm. This conversion uses 100 cm per metre, not the 1000 used for litres and millilitres.

Check your understanding 2 Show both parts

Write 3070 ml as litres and millilitres. Take out every complete litre, leaving fewer than 1000 ml in the millilitres part.

Litres

Millilitres left over

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3 ℓ 70 ml. Three litres account for 3000 ml, leaving 70 ml. The check is 3 × 1000 + 70 = 3070. Both parts together make the original volume.

Compare after making the units match

Which has greater mass: 2 kg 50 g or 1950 g? The first is 2050 g, so it is greater by 100 g. Comparing only “2” with “1950” ignores the different units.

Check your understanding 3 A mixed-unit subtraction

A jug has 2 ℓ 100 ml of water. You pour out 450 ml. How much remains? Give your answer in millilitres and in compound units.

Your two measurements and check, or work on paper

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2 ℓ 100 ml is 2100 ml. Subtracting gives 2100-450 = 1650 ml, or 1 ℓ 650 ml. Check that the amount poured plus the amount remaining is 2100 ml.

Measure before converting

Read an actual tape, scale or measuring jug using its marked unit. Record the original measurement before changing its units, so you can check whether the conversion kept the same physical amount. A calculation here does not verify how accurately you used the instrument.