Units of Measure

Meters, Centimeters and Kilometers #

Built from one hundred and one thousand.

The metric lengths are built from one hundred and one thousand

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This ruler is 10 cm long, and ten of them make 100 cm — that is 1 meter.

Kilo means a thousand: 1000 m = 1 km.

Converting Lengths #

Same length, smaller unit, bigger number.

A length never changes when you change its unit — only the number counting it does

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Here is a length: 3 meters.

Now measure the very same length with a smaller unit.

3 m is 3 × 100 = 300 cm.

Each unit is worth a fixed amount. Look it up, then multiply.

Converting Units of Area #

The square catches both factors.

An area converts once for each direction, so the length factor gets squared

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A meter is 100 cm, so a 1 m square is 100 cm by 100 cm: 10,000 cm², not 100.

An area converts once for each of its two directions.

The same square catches every pair: 1 cm² is 10 mm by 10 mm — 100 mm².

A volume converts three times over: $1m^3=1,000,000$1 m³ = 1,000,000 cm³.

Grams and Kilograms #

A thousand grams sit inside every kilogram.

A thousand grams sit inside every kilogram

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The scale does not move: 1 kg = 1000 g, the same weight twice.

So 1 kg 500 g = 1500 g: the kilogram becomes 1000 g and the 500 joins it.

Milliliters and Liters #

A thousand milliliters fill the bottle.

A thousand milliliters fill a one liter bottle

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Full to the top reads 1 L on the left and 1000 mL on the right.

Pour some out. The level is a quarter: 0.25 L on the left, 250 mL on the right.

Reading Scales #

Work out what one small mark is worth first.

Work out what one small mark is worth before reading any scale

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5 gaps share 100, so each gap is worth 20. The arrow sits 3 gaps along, at 60.

3 small marks cut the 20 gap into 4 steps of 5, and the arrow sits 2 past 40: 50.

$100/4=25\text{a}$100 / 4 = 25 a step, so 2 steps past 200 reads 250 g.

Time Durations #

Count up to the hour, then past it.

Count up to the next hour first, then carry on past it

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A film starts at 3:40pm and ends at 4:10pm. How long does it last?

20 minutes reach 4:00pm, then 10 minutes more: 20 + 10 = 30.

Money as Decimals #

Cents are hundredths you can hold.

Cents are hundredths of a dollar with coins to hold

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$3.45 is 3 whole dollars and 45 cents. The dot splits the dollars from the cents.

45 cents is 45 hundredths of a dollar: $0.45.

Estimating with Units #

A number that could actually be true.

Choose the unit first, then a number that could actually be true

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A pencil is about 15 centimeters. Not meters — a 15 m pencil would cross the road.

An apple weighs about 150 g. Not kilograms — a 150 kg apple outweighs two adults.