Question

How do you change 0.244444444 into a fraction?

Answer 1

This is the technique also for dealing more difficult ones. You have to decide what to multiply by guided by the repeat cycle.

Explanation:

Let `x = 0.244444....`..............(1)

so `10x = 2.44444`.....(2)

(2) - (1)

`10x -x=2.2`
`9x =2 2/10`

`x= 2/9 + 2/90`

`x = (20+2)/90`

`x=22/90`

`x=11/45`

Answer 2

Convert into a terminating continued fraction, then simplify to find

`0.2dot(4) = 11/45`

Explanation:

`0.2dot(4)` is less than `1` so the continued fraction starts `0 + 1/...`

Calculate `1/(0.2dot(4)) = 4.dot(0)dot(9)`

So our continued fraction looks like `0+1/(4+1/...)`

Subtract `4` then calculate `1/(0.dot(0)dot(9)) = 11`

So our fraction terminates here in the form: `0+1/(4+1/11)`

`0+1/(4+1/11) = 1/(44/11+1/11) = 1/(45/11) = 11/45`