Moving the Point

A road sign says the next town is 2.5 km away. Your friend asks: "How many metres is that?" With older units this would mean some careful sums. With metric units you can answer in a second. How?

Multiplying by ten is moving the point

In the Kilo, Centi, Milli lesson we saw that every metric step is 10, 100 or 1,000. Multiplying by these numbers is easy:

times 10: move the point one place to the right;
times 100: move the point two places;
times 1,000: move the point three places.

When there are no more digits, write zeros. So 2.5 times 1,000: move the point three places to the right, filling the empty places with zeros, and you get 2,500.

A kilometre is 1,000 metres, so 2.5 km = 2,500 m.

Changing 2.5 kilometres into metres: one kilometre is 1,000 metres, so the point moves three places to the right, filling the empty places with zeros, and 2.5 becomes 2,500

Which way does the point go?

In the A Number and a Unit lesson we saw that a smaller unit gives a bigger number. That tells you which way to move:

to a smaller unit (km to m, m to cm): the number gets bigger, so the point moves to the right;
to a bigger unit (mm to cm, cm to m): the number gets smaller, so the point moves to the left.

A pencil is 150 mm long. Going to centimetres, a bigger unit, the number gets smaller: 10 mm make a centimetre, so move the point one place left. 150 mm = 15 cm.

A door is 210 cm tall. 100 cm make a metre, so move the point two places left. 210 cm = 2.1 m.

The staircase

Here are the steps between the lengths you know. Going down the stairs, to a smaller unit, the point moves right. Going up, to a bigger unit, it moves left.

A staircase of length units: kilometre at the top, then metre, centimetre and millimetre. From km to m is times 1,000, from m to cm times 100, and from cm to mm times 10. Going down, the number gets bigger; going up, it gets smaller

Try it at home

Measure a book in millimetres. Now write the same length in centimetres by moving the point one place left. Check with the ruler.
Change these, then check your answers at the bottom: 3 km into metres; 400 cm into metres; 7 cm into millimetres.

Answers: 3,000 m; 4 m; 70 mm.

Words to know

converting units - writing the same measurement in a different unit, like 2.5 km as 2,500 m

Big idea

Changing between metric units is moving the point: one place for 10, two for 100, three for 1,000. To a smaller unit the number gets bigger and the point moves right; to a bigger unit, left.