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Metric conversions

mm, cm, m and km; g and kg; ml and l; including squared and cubed units.

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How long is a pencil? How heavy is a bag of sugar? How much does a jug hold? We measure with units, and the metric units all work in tens, hundreds and thousands. That makes changing from one unit to another a job for Lesson 1.2: the digits move, and the point stays still. In this lesson you will learn how to:

  • choose a sensible unit for length, mass and capacity
  • read a ruler in centimetres and millimetres
  • convert by multiplying or dividing by 10, 100 or 1000
  • read the scales on a jug and a kitchen scale
  • compare and order amounts in different units
  • solve problems with mixed units
  • convert squared and cubed units
Dark blue: whole numbers Red dot: the decimal point Blue: digits after the point

1. Metric units: how big is each one?

Key idea Length is how long something is, mass is how heavy it is and capacity is how much it can hold. The start of a unit’s name tells you its size: kilo means a thousand, centi means a hundredth and milli means a thousandth. So a kilometre is 1000 metres, and a millimetre is a thousandth of a metre.
Length: how longMass: how heavyCapacity: how much it holds
mm millimetreg gramml millilitre
cm centimetrekg kilograml litre
m metre
km kilometre

The facts to learn

1 cm = 10 mm1 m = 100 cm1 km = 1000 m1 kg = 1000 g1 l = 1000 ml

And because 1 m = 100 cm and 1 cm = 10 mm, 1 m = 1000 mm.

Get a feel for the sizes

  • 1 mm is about the thickness of a bank card.
  • 1 cm is about the width of your little fingernail.
  • 1 m is about one big stride. A door is about 2 m tall.
  • 1 km is about 12 to 15 minutes of walking.
  • 1 g is about a paperclip. 1 kg is a bag of sugar.
  • 1 ml is a few drops. A teaspoon holds 5 ml. 1 l is a big bottle of water.
Watch out Grams and kilograms measure mass; millilitres and litres measure capacity. A mug holds 300 ml, not 300 g. Pick the kind of unit first, then its size.

2. Lengths on a ruler

Key idea On a ruler, each centimetre is cut into 10 millimetres. Line the start of the thing up with 0. Count the whole centimetres, then the small marks after them.

Example: how long is the pencil?

0123456789101112131415cm
  1. The pencil ends after 7 whole centimetres, and 4 small marks more:7 cm 4 mm
  2. In millimetres: 7 cm is 7 × 10 = 70 mm, and 4 more:74 mm
  3. In centimetres: 4 mm is 4 tenths of a centimetre:7.4 cm
AnswerThe pencil is 7 cm 4 mm, which is 74 mm or 7.4 cm.
Watch out 7 cm 4 mm is 7.4 cm, not 7.04 cm. There are only 10 mm in a centimetre, so each millimetre is a tenth: the first column after the point.

3. Converting: the unit stairs

Key idea Going down the stairs, to a smaller unit, you need more of them, so you multiply. Going up, to a bigger unit, you need fewer, so you divide. The digits move and the decimal point stays still, just as in Lesson 1.2.
kmkilometres× 1000÷ 1000mmetres× 100÷ 100cmcentimetres× 10÷ 10mmmillimetres
kgkilograms× 1000÷ 1000ggrams llitres× 1000÷ 1000mlmillilitres

Example 1: change 3.45 m into cm

  1. Centimetres are smaller, so there will be more of them. 1 m = 100 cm:× 100
  2. The digits move 2 places to the left:3.45 × 100 = 345
Answer3.45 m = 345 cm

Example 2: change 2500 g into kg

  1. Kilograms are bigger, so there will be fewer of them. 1 kg = 1000 g:÷ 1000
  2. The digits move 3 places to the right:2500 ÷ 1000 = 2.5
Answer2500 g = 2.5 kg
Watch out Use the right number for the step. Metres to centimetres is × 100, not × 1000. And keep the zeros: 45 g is 0.045 kg, because 45 ÷ 1000 moves every digit 3 places.

4. Reading scales: jugs and kitchen scales

Key idea Not every mark on a scale has a number. Take two numbers next to each other and find the difference. Count the gaps between them, then share: that is what each small mark is worth.

Example: how much water is in the jug?

02004006008001000ml
  1. From 400 to 600 is 200 ml, and there are 4 gaps:200 ÷ 4 = 50
  2. Each small mark is 50 ml. The water is 3 marks above 400:400 + 150 = 550
Answer550 ml, which is 0.55 l.

And on a kitchen scale

01002003004005006007008009001000g

The numbers go up in 100s, with one mark between them, so each mark is 50 g. The needle is on the mark between 300 and 400: 350 g.

Watch out Count the gaps, not the marks. Between 400 and 600 there are 3 small marks but 4 gaps.

5. Comparing and ordering

Key idea You can only compare amounts in the same unit. Change them all into the smaller unit first, so there are no decimals. Then compare the numbers.

Example: put 1.2 kg, 950 g, 1050 g and 0.8 kg in order, lightest first

  1. Change the kilograms into grams (× 1000):1.2 kg = 1200 g, 0.8 kg = 800 g
  2. Now they are all grams:1200, 950, 1050, 800
  3. Order the numbers:800 < 950 < 1050 < 1200
Answer0.8 kg, 950 g, 1050 g, 1.2 kg
Watch out The biggest number is not always the biggest amount. 0.5 km is 500 m, which is more than 50 m and the same as 50,000 cm.

6. Problems with mixed units

Key idea Before you add, take away or share, put everything into one unit. “3 m 45 cm” means 3 metres and 45 centimetres: that is 345 cm, or 3.45 m.

Example 1: a jug holds 1.5 l of juice. Sam pours 3 glasses of 250 ml. How much is left?

  1. Change the litres into ml:1.5 × 1000 = 1500 ml
  2. Three glasses:3 × 250 = 750 ml
  3. Take it away:1500 − 750 = 750 ml
Answer750 ml is left.

Example 2: how many 25 cm pieces can you cut from 3 m of ribbon?

  1. Change the metres into cm:3 × 100 = 300 cm
  2. Share it into 25s:300 ÷ 25 = 12
Answer12 pieces.
Watch out 2 kg 50 g is 2050 g, or 2.05 kg. It is not 2.5 kg: 50 g is only 50 thousandths of a kilogram, so it needs the 0 in the tenths column.

7. Squared and cubed units

Key idea 1 cm2 (a square centimetre) is a square 1 cm by 1 cm. Each side is 10 mm, so it holds 10 rows of 10 tiny squares: 1 cm2 = 100 mm2. A cubic centimetre, 1 cm3, is a cube with 10 layers of 100: 1 cm3 = 1000 mm3.

1 cm2 = 10 × 10 = 100 mm2

1 cm = 10 mm1 cm = 10 mm

1 cm3 = 10 × 10 × 10 = 1000 mm3

1 cm = 10 mm

The squared and cubed facts

LengthSquared (area)Cubed (volume)
1 cm = 10 mm1 cm2 = 10 × 10 = 100 mm21 cm3 = 10 × 10 × 10 = 1000 mm3
1 m = 100 cm1 m2 = 100 × 100 = 10,000 cm21 m3 = 100 × 100 × 100 = 1,000,000 cm3

Capacity and cubed units meet here: 1 ml = 1 cm3. A cube 10 cm by 10 cm by 10 cm is 1000 cm3, and it holds exactly 1 litre.

Watch out 1 cm2 is not 10 mm2. The 10 mm is along one side; a square has two sides multiplied together, so it is 10 × 10 = 100. For cubes, multiply three times.

The mistakes that cost marks

  1. Using the wrong number for the step. Multiplying by 1000 to change metres into centimetres. learn the facts: 1 m = 100 cm, 1 cm = 10 mm, and the thousands for km, kg and l.
  2. Going the wrong way. Dividing to change kg into g, so 3 kg becomes 0.003 g. a smaller unit needs more of them: multiply. Ask “should my number get bigger?”
  3. Losing the zeros. Writing 45 g as 0.45 kg. move every digit 3 places for ÷ 1000: 0.045 kg.
  4. Mixed units read as a decimal. Writing 2 kg 50 g as 2.5 kg. change the whole lot into grams first: 2000 + 50 = 2050 g = 2.05 kg.
  5. Counting marks, not gaps. Saying each mark is 200 ÷ 3 when there are 3 marks between two numbers. count the gaps: 3 marks make 4 gaps, so 200 ÷ 4 = 50.
  6. Comparing different units. Saying 950 g is more than 1.2 kg because 950 is bigger than 1.2. put both into the same unit first: 1.2 kg = 1200 g.
  7. Squared units with one 10. Writing 1 cm2 = 10 mm2. square the number: 10 × 10 = 100 mm2; cube it for cubed units: 1000 mm3.
  8. Leaving off the unit. Writing 750 when the answer is 750 ml. always write the unit, and check it is the one the question asked for.

Quick checklist

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