Question

What is `0.444...` as a fraction?

Answer 1

`0.444... = 4/9`

Explanation:

Given:

`0.444...`

Notice what happens if we multiply it by `10`:

`10 * 0.444... = 4.444...`

So if we subtract the original we cancel out the tail...

`10 * 0.444... - 0.444... = 4.444... - 0.444... = 4`

Now:

`10 * 0.444... - 0.444... = 10 * 0.444... - 1 * 0.444...`

`color(white)(10 * 0.444... - 0.444...) = (10-1)*0.444...`

`color(white)(10 * 0.444... - 0.444...) = 9*0.444...`

So:

`9 * 0.444... = 4`

Divide both sides by `9` to find:

`0.444... = 4/9`