Unit conversions — introduction

Unit conversions — introduction

Unit conversions

Imagine telling a friend that your school is "1 500 long". Long what? Steps? Metres? Kilometres? Without a unit the number means nothing. Units tell us what we are counting. And because the same length can be written as 1 km, 1 000 m or 100 000 cm, we often need to convert a number from one unit to another.

Why we have so many units

Different units suit different sizes.

  • We measure the length of a pencil in centimetres, not kilometres.
  • We weigh an apple in grams, not tonnes.
  • We pour juice in millilitres, not litres-with-many-zeros.

Picking the right unit keeps numbers small and easy to read.

The ladder of tens

For length, mass and volume we use the metric system. Each unit is ten times bigger than the one below it (with a few skips). That gives us a clean ladder you can climb up or down.

LengthMassVolume
1 km = 1 000 m1 t = 1 000 kg1 l = 1 000 ml
1 m = 100 cm1 kg = 1 000 g1 l = 10 dl
1 m = 1 000 mm1 kg = 100 dag1 dl = 100 ml
1 cm = 10 mm1 dag = 10 g1 dl = 10 cl

Time is the odd one out — minutes and hours use 60s, days use 24s. We'll meet time later on its own page.

When to multiply, when to divide

There is one rule for the whole ladder.

  • Going down the ladder (from a big unit to a small one) — multiply. There are more small pieces in one big piece. 3 m = 3 × 100 cm = 300 cm.
  • Going up the ladder (from a small unit to a big one) — divide. Many small pieces make one big piece. 4 000 g = 4 000 ÷ 1 000 = 4 kg.

💡 A quick mental check: if the new number looks bigger than the old one, you switched to a smaller unit. If it looks smaller, you switched to a bigger unit.

A worked example

Maya runs 2 km. Her little brother runs 800 m. Who ran further?

Both numbers need the same unit before we can compare them. Convert 2 km to metres:

2 km = 2 × 1 000 m = 2 000 m.

Now compare 2 000 m and 800 m. Maya ran further by 1 200 m.

What you will learn

Try it out