Question

How do you change 0.5625 into a fraction?

Answer 1

Since this decimal ends with `5`, see what happens when we multiply by `2`, then by `2` again, etc., eventually finding:

`0.5625 = 9/16`

Explanation:

Let's take this step by step to keep the arithmetic simple and avoid introducing unnecessary common factors...

`0.5625` ends in `5`, so multiply it by `2`:

`0.5625 xx 2 = 1.125` which ends in `5`, so multiply by `2` again:

`1.125 xx 2 = 2.25` which ends in `5`, so multiply by `2` again:

`2.25 xx 2 = 4.5` which ends in `5`, so multiply by `2` again:

`4.5 xx 2 = 9`

Having reached a whole number, notice that we have multiplied by `2` four times.

So:

`0.5625 = 9/(2^4) = 9/16`

In general, if a decimal ends with `5`, multiply it by `2`. If it ends with an even digit, multiply it by `5`. Otherwise multiply by `10`.

Repeat until you get a whole number, then that is the numerator and the denominator is the product of the multipliers you used.

For example,

`0.24 stackrel(xx 5) -> 1.2 stackrel(xx 5) -> 6`

So `0.24 = 6/(5^2) = 6/25`