Between Systems

You are on holiday in the United Kingdom, and the road sign says "Oxford 10 miles". Your phone's map, set up at home, says kilometres. Or your friend in the United States says their new TV is 50 inches. How big is that in centimetres?

Moving the point won't help here, because these older units don't go in tens. But a few rough rules will.

Miles and kilometres

In the Inches, Feet and Miles lesson we saw that a mile is about 1.6 kilometres - a bit more than one and a half.

Miles into kilometres take the number, add half of it, then add a little more.

10 miles: 10, plus half of 10 (5), is 15; a little more makes about 16 km.
20 miles: 20 + 10 = 30, a little more: about 32 km.

Kilometres into miles go the other way, and take a bit more than half.

10 km: half is 5, a bit more: about 6 miles.
A "5K" running race, 5 km, is about 3 miles.

A road sign saying Oxford 10 miles, and the trick: 10, plus half of 10 is 15, plus a little more is about 16 kilometres

Inches and centimetres

An inch is about 2 and a half centimetres.

Inches into centimetres double the number, then add half of the number.

10 inches: double is 20, plus half of 10 (5), is about 25 cm.
12 inches (one foot): 24 + 6 = about 30 cm, just as we saw.
That 50-inch TV: 100 + 25 = about 125 cm, corner to corner.

How close is "about"?

These rules are not exact, and they don't need to be. For a road trip or a TV, "about 16 km" is plenty: the real answer for 10 miles is 16.09 km. When something must be exact - building a bridge, or sending a spacecraft to another planet - people use exact numbers, and the safest choice is for everyone to use the same units in the first place. The last lesson of this course is about what happened when two teams didn't.

Try it at home

Use the miles trick on 30 miles and 100 miles.
Use the inches trick on a 32-inch screen.
Check your answers with a phone calculator: multiply miles by 1.6, and inches by 2.54. How close did you get?

Words to know

rough rule - a quick way to get an answer that is close, but not exact

Big idea

Older units don't go in tens, so you can't just move the point. Rough rules get close in your head: a mile is about 1.6 km (add half and a bit), and an inch about 2.5 cm (double, then add half).