Measures
Converting lengths, masses and amounts of liquid, comparing amounts in mixed units, imperial units and reading scales: the quick way to answer each, and the traps the wrong answers set.
Chapter 1
What are measures questions?
A measure is an amount and its unit: 6900 m, 2.5 kg, 330 ml. The unit says what you’re counting in. Change the unit, and the number changes too.
The amount. 6900 m: six thousand nine hundred metres.
The unit it wants. Here it’s km, kilometres. The same distance in a bigger unit.
Other questions compare amounts in different units, use imperial units like pints and miles, or ask you to read a scale. This page covers them all. Time and money have their own page.
6900 m = ? km
The options
- Option 1: 0.069
- Option 2: 69
- Option 3: 6.9
- Option 4: 6900
A Maths question from Rush, level 3.
The units to know
Kilo means a thousand, centi a hundredth and milli a thousandth. So a kilometre is 1000 m, a centimetre is a hundredth of a metre, and a millilitre a thousandth of a litre.
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Length how long
A fingertip is about 1 cm wide, and a door about 2 m tall.
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Mass how heavy
A paperclip weighs about 1 g, and a bag of sugar 1 kg.
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Capacity how much it holds
A teaspoon holds about 5 ml, and a can of drink 330 ml. L and l both mean litres.
Chapter 2
Solve it in 3 steps.
Here’s the question, one step at a time.
The question
6900 m = ? km
The options
- Option 1: 0.069
- Option 2: 69
- Option 3: 6.9
- Option 4: 6900
A Maths question from Rush, level 3.
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Step 1
Find the step.
How many metres make a kilometre? Kilo means a thousand, so 1000.
1000 m make 1 km.
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Step 2
Bigger unit? Divide.
A kilometre is bigger than a metre, so it takes fewer of them: divide by 1000. That’s three ÷ 10s, so every digit moves 3 places right.
1000 has three zeros: three hops.
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Step 3
Check the size.
6900 m is just under 7000 m, which is 7 km. So the answer is just under 7, and 6.9 km fits.
6 whole kilometres and most of the next.
Three mistakes this question sets
| The mistake | Do this instead |
|---|---|
| Using 100, not 1000. 69 is 6900 ÷ 100, the step for centimetres to metres. | 1 km = 1000 m. Three zeros, three places. |
| Moving too far. 0.069 moves the digits 5 places. 0.069 km is only 69 m. | Count the zeros in the step, not in the amount. |
| Changing only the unit. 6900 km is a thousand times too far: a new unit needs a new number. | Bigger unit, smaller number. Always. |
So it’s 6.9 km. 6900 ÷ 1000 = 6.9, just under 7 km, as step 3 said.
Remember: Bigger unit, smaller number.
Chapter 3
Everything else Rush asks.
Each card is one kind of question: the rule, one worked example, and the trap. Most need the same two things: the step, and which unit is bigger.
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- 9 L = 9000 ml
- 0.75 L = 750 ml
- 9.75 L = 9750 ml
Smaller unit? Multiply.
A smaller unit takes more of them, so multiply by the step.
9.75 L = ? ml. Multiply by 1000: every digit moves 3 places left, so 9750 ml. Traps: 9000, which forgets the 0.75 L, and 975, from × 100.
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- 1 m 6 cm = 106 cm
- 1 m 6 cm = 1.06 m
Two units at once
Change the big unit, then add the small one.
1 m 6 cm is 100 + 6 = 106 cm. As metres, 6 cm is 0.06 m, so it’s 1.06 m. Trap: 1.6 m, which is 160 cm.
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2700 g 2700 g 2.9 kg 2900 g 2 kg 400 g 2400 g 2800 g 2800 g Which is heaviest?
Change them all to the smaller unit. Then compare.
In grams, 2.9 kg is 2900 g, the heaviest. Rush asks for the longest, shortest, lightest and “which jug holds the most” too. Trap: 2800 g, the biggest number on show.
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- 5 kg = 5000 g
- 5000 g − 200 g = 4800 g
Taking away across units
Change the big one into the small unit first.
5 kg − 200 g: 5 kg is 5000 g, so 4800 g. Trap: 300, from treating 5 kg as 500 g. Rush asks these in Add & Subtract.
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Imperial units
Their steps aren’t 10s. Learn them.
9 gallons = ? pints. 8 pints make a gallon, so 9 × 8 = 72. Going back, divide: 80 pints is 10 gallons. Traps: 90, from using 10, and 17, from 9 + 8.
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Imperial to metric
The question gives the rate. Multiply by it.
1 mile is about 1.6 km. About how many km is 3 miles? 3 × 1.6 = 4.8 km. Trap: 48 or 0.48, the point moved. 3 miles is a few km, so 4.8 fits.
Learn these by heart
≈ means “is about”. Knowing these spots a silly answer. Square units use the step twice: a square metre is 100 cm by 100 cm, so 10,000 cm², not 100.
- Roughly the same
- 1 inch ≈ 2.5 cm1 foot ≈ 30 cm1 mile ≈ 1.6 km1 kg ≈ 2.2 pounds1 pint ≈ 0.6 L1 gallon ≈ 4.5 L
- Square and cubic
- 1 cm² = 100 mm²1 m² = 10,000 cm²1 cm³ = 1 ml1 L = 1000 cm³
Chapter 4: In the exam
Answers with units.
The exam puts a unit change inside a short story, and its options carry units. Rush asks the steps one at a time.
- A1.15 kg
- B450 kg
- C0.45 kg
- D4.5 kg
- E1.05 kg
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Step 1
Make the units match.
Two amounts are in grams, so change the bag into grams too: 1.5 kg is 1500 g.
1.5 kg=1500 g
× 1000: kg to g.
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Step 2
Work out what’s used.
3 cakes of 350 g: 3 × 350 = 1050 g.
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Step 3
Take it away.
1500 − 1050 = 450, so 450 g is left. Check: 1050 + 450 = 1500.
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Step 4
Find it in the options.
450 g isn’t there. Change it back: 450 ÷ 1000 = 0.45, so it’s 0.45 kg, option C.
450 g=0.45 kg
The same amount, in the options’ unit.
Three mistakes this question sets
| The mistake | Do this instead |
|---|---|
| The right number, the wrong unit. 450 kg has the right digits, but it’s a thousand times too heavy. | Read the unit on every option, not just the number. |
| Using 100, not 1000. 4.5 kg is 450 ÷ 100. | 1 kg = 1000 g, so three places. |
| Stopping early. 1.05 kg is the flour used. 1.15 kg is what’s left after just one cake. | Read the question again: what’s left after all 3. |
So it’s C, 0.45 kg. That’s 450 g, written in kilograms.
Remember: Check the number and the unit.
Other ways the exam asks it
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Reading a scale
Work out what one small mark is worth first.
The numbers go up in 200s, with 4 spaces between, so each mark is 200 ÷ 4 = 50 g. 3 marks past 200 is 350 g. Trap: 230 g, counting the marks as 10s.
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25 ml250 ml2.5 L25 L
Sensible estimates
Compare it with something you know.
How much does a mug hold? A can of drink is 330 ml, and a mug holds about that, so 250 ml. Trap: 25 ml is only five teaspoons.
Chapter 5
Try it yourself.
Six real questions from Rush, easy to hard, 60 seconds on the clock.
Use the steps
- Find the step.
- Bigger unit? Divide.
- Check the size.
Remember: Bigger unit, smaller number.
For parents.
What parents ask us about measures.
Questions parents ask
What units of measurement does my child need to know for the 11+?
Millimetres, centimetres, metres and kilometres for length, grams and kilograms for mass, and millilitres and litres for capacity, with how to convert between them. That is Year 5 and Year 6 national curriculum, which also asks roughly how metric units compare with inches, pounds and pints, and how to convert between miles and kilometres.
How do you know whether to multiply or divide?
Ask which unit is bigger. A kilogram is bigger than a gram, so the same amount needs fewer kilograms: 3500 g is only 3.5 kg. If your answer is a bigger number in the bigger unit, it has gone the wrong way.
What's the easiest way to remember metric conversions?
Learn what the start of each word means. Kilo is a thousand: a kilometre is 1000 metres and a kilogram 1000 grams. Centi is a hundredth, so there are 100 centimetres in a metre. Milli is a thousandth, so there are 1000 millilitres in a litre and 1000 millimetres in a metre.
Does my child need to learn imperial to metric conversions by heart?
Rush's questions give the rate, such as 1 inch is about 2.5 cm, so all it takes is one multiplication. It still helps to know a few rough ones, so a child can spot a silly answer: a mile is a bit over 1.5 km, a kilogram a bit over 2 pounds, a pint a bit over half a litre.
Rush: 11+ Practice & KS2 SATsPractise measures in Rush.
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