Question

What is 72.1 repeating as a fraction

Answer 1

`x=72.\overline{1}\\ 10x=721.\overline{1}\\ 10x-x=721.\overline{1}-72.\overline{1}\\ 9x=649\\ x=(649)/(9)`

Answer 2

Let

`x=72.111...`

Multiply x by a power of
`10`, one that keeps the decimal part of the number the same:

`10x=721.111..`

Subtract
`x` from
`\\10x`

`10x-x=721.111-72.111=649`

The repeating decimals should cancel out

`\\9x=649`

solve for x

Divide by
`9` both sides

`9x/9=649/9`

`x=649/9`

therefore

the answer is

The fraction is
`(649)/(9)`