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

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

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

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$1 m³ = 1,000,000 cm³.

Grams and Kilograms #

A thousand grams sit inside every kilogram.

A thousand grams sit inside every kilogram

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

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

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

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

$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

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.