KS3 · Maths

Place value in metric and imperial units

Same length, two ways: 6 cm and 0.06 m. The 6 is unchanged, yet it is now worth six hundredths, not six ones. The unit decides a digit's worth.

Maths · Measures

One journey, four units
0 km2 km4 km6 km8 km10 km12 km14 km16 km18 km20 kmDrag the handle along the bar

Distance in kilometres: 16/20. Kilometres 16 km. Metres (km × 1,000) 16,000 m. Centimetres (m × 100) 1,600,000 cm. Millimetres (cm × 10) 16,000,000 mm

Kilometres16 kmMetres (km × 1,000)16,000 mCentimetres (m × 100)1,600,000 cmMillimetres (cm × 10)16,000,000 mm

Drag the handle. Kilometres to metres multiplies by 1,000, metres to centimetres by 100, and centimetres to millimetres by 10 — so each time the unit gets smaller, the number gets bigger.

Watch out: 16 km is 16,000 m, not 160 m. 160 m is a short walk down the road, not a drive to work — so check your answer against something real.

The place value chart: the digits stay put, the unit moves the point

Problem

Convert 12 metres into centimetres using a place value chart.

Maths · Choosing a unit

Which unit would you reach for?

Pick a situation, then pick the metric unit that suits it. You commit first and read the reason after.

Still to sort

kilometres (km) (0)

a thousand times as long as a metre

centimetres (cm) (0)

a hundredth of a metre

litres (l) (0)

the standard unit of capacity

millilitres (ml) (0)

a thousandth of a litre

grams (g) (0)

the standard unit of mass

5 of 5 still to sort.

Metric units are built on three standard units: the metre (m) for length, the gram (g) for mass and the litre (l) for capacity. A prefix then makes them bigger or smaller, and the unit you choose tells people how big the thing is.

Watch out: The unit gives a clue about size. If you picked kilometres for a child's height, the number would look silly — that is your warning.

Maths · Comparing measures

Put mixed capacities on one line

This line is in litres. Drag each capacity to where it belongs. Some are written in millilitres, so convert before you drag.

Metric and imperial side by side

MetricvsImperial

Start with the biggest difference: how each system converts.

Focus

How you convert

Metric

Always × or ÷ 10, 100 or 1,000

Imperial

A different multiplier for each pair: 3, 12, 14, 16

The insight

This is the big one. Imperial does not convert by powers of 10, so 'times ten' is the wrong reflex.

Prefixes

Metric

kilo, centi and milli tell you the size

Imperial

None — no kilo, centi or milli

Units of length

Metric

millimetres, centimetres, metres, kilometres

Imperial

inches, feet, yards, miles

Where the units come from

Metric

Built on three standard units: the metre, the gram and the litre

Imperial

An older system that evolved over history. The foot was once based on a human foot, so units were standardised in the 1800s: 1 foot is exactly 12 inches

Who uses it

Metric

Most countries in the world

Imperial

The USA (miles, pounds, gallons). The UK uses a mixture of both

Maths · Imperial conversions

Spot the metric reflex

Convert 3 yards into inches.

A student's working — which line goes wrong?

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

The unit decides what every digit is worth.

What you need to know

  • Metric units are built on the metre (m), gram (g) and litre (l). Kilo means 1,000 times, centi means one hundredth and milli means one thousandth.
  • The unit decides the place value of each digit: 8 mm is eight thousandths of a metre, 0.008 m.
  • To convert, either use a place value chart (the digits stay put and the decimal point moves) or multiply or divide by the prefix's multiplier.
  • To compare measures, convert them into the same unit first, then check the size against something real.
  • Imperial units have no prefixes. Each pair needs its own multiplier: × 3, × 12, × 14 and × 16.

The big picture

A measure's unit decides what each digit is worth. Metric units are built on the metre, gram and litre, and the prefixes kilo (× 1,000), centi (one hundredth) and milli (one thousandth) are fixed multipliers. Imperial units have no prefixes, so each pair of units has its own multiplier.

Key points

1A prefix is a fixed multiplier: kilo × 1,000, centi one hundredth, milli one thousandth.
2Kilometres to metres is × 1,000, metres to centimetres × 100, centimetres to millimetres × 10.
3When the unit gets smaller the number gets bigger, so 16 km is 16,000 m, not 160 m.
4Metric converts by 10, 100 or 1,000. Imperial does not: yards to feet × 3, feet to inches × 12, stones to pounds × 14, pounds to ounces × 16.
5Imperial grew out of an older system, with units like the foot standardised in the 1800s so that 1 foot is exactly 12 inches.

Worked example

Problem

A parcel has a mass of 3.4 kg. Write its mass in grams, and check that your answer is the right size.

⚠ Watch out

Believing every unit converts by 10. Metric prefixes are fixed multipliers (kilo is 1,000, not 10), which is why 16 km is 16,000 m and not 160 m. Imperial is different again: a foot is 12 inches, not 10.

🧠

Memory hook

Kilo = a thousand, centi = a hundredth, milli = a thousandth. And imperial? No prefixes, so learn the multipliers: 3, 12, 14, 16.

✓

Check yourself

A jug holds 0.75 litres. How many millilitres is that, and should your number be bigger or smaller than 0.75? (750 mL: bigger, because a millilitre is only a thousandth of a litre.)

Flashcards

(15)
Which three standard units is the metric system built around?
The metre (m) for length, the gram (g) for mass and the litre (l) for capacity.
What does the prefix kilo mean?
1,000 times. A kilometre is a thousand times as long as a metre, and 1 kg = 1,000 g.
What does the prefix centi mean?
One hundredth. A centimetre is a hundredth of a metre, so the metre is a hundred times larger.
What does the prefix milli mean?
One thousandth. A millimetre is a thousandth of a metre; a millilitre is a thousandth of a litre.
Name the four metric units of length, smallest to largest.
Millimetres, centimetres, metres, kilometres.
Name the three metric units of mass.
Milligrams, grams and kilograms.
Name the three metric units of capacity.
Millilitres, centilitres and litres.
Why does 8 mm become 0.008 m?
A millimetre is a thousandth of a metre, so in metres the 8 sits in the thousandths column. The unit decides the digit's place value.
What are the moves of the place value chart method?
Ones digit into the original unit's column, other digits to match, placeholder zeros up to the new unit's column, decimal point to the right of that column.
How do you compare 0.82 L with 820 mL?
Convert them to the same unit first. 0.82 litres is 820 millilitres, so they are exactly the same capacity.
How can you check that a conversion is the right size?
Compare it with something real: a door is about 2 m, a bag of sugar is 1 kg = 1,000 g, and 160 m is a short walk down the road.
Name the imperial units of length, smallest to largest.
Inches, feet, yards, miles.
Name the imperial units of mass and of capacity.
Mass: ounces, pounds, stone. Capacity: fluid ounces, pints, gallons.
What multipliers do these imperial conversions use?
Yards to feet × 3, feet to inches × 12, stones to pounds × 14, pounds to ounces × 16. Going the other way uses division.
Who uses metric and who uses imperial?
Most countries use metric. The USA uses imperial. The UK uses a mixture, depending on the context.

Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.

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