Turning a fraction into a decimal

Neenu has 29 metres of red ribbon and wants to share it equally with Anu. How much does each get? Each gets 29 ÷ 2 metres.

Think it through in parts. If each gets 14 m, that uses 28 m and 1 m remains. Dividing that 1 m between two gives each another 1/2 m.

So how do we write 1/2 as a decimal? It is easy to express a fraction as a decimal when the denominator is 10, 100 or 1000. Can we find an EQUIVALENT fraction with such a denominator?

We can: 1/2 = (1 × 5)/(2 × 5) = 5/10, multiplying numerator and denominator by 5. And 5/10 is 0.5. So each girl gets 14 + 0.5 = 14.5 m.

Now share the same 29 m among FOUR friends. Each gets 29 ÷ 4 m, that is 29/4. The denominator is 4. Is 4 a factor of 10? No. Is it a factor of 100? Yes — 4 × 25 = 100.

So multiply numerator and denominator by 25: (29 × 25)/(4 × 25) = 725/100 = 7.25. Each of the four friends gets 7.25 m.

The method is quick when it works: find what to multiply the denominator by to reach a power of ten, multiply the numerator by the same, and read off the decimal. Try 2/5, 13/4, 4/50 and 5/8. But note the condition — the denominator must divide some power of ten. That will not always be so, which is what the next lesson has to deal with.