Question

Find an equivalent fraction for the decimal number. In your final answer, include all of your work.

0.901 recurring

Answer 1

`(901)/(999)`

Explanation:

we know that

A Recurring Decimal, is a decimal number with a digit (or group of digits) that repeats forever.

In this problem we have

0.901 recurring

that means

0.901901901..

Let

`x=0.901901901..`

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

`1,000x=901.901901..`

Subtract
`x` from
`\\1000x`

`1,000x-x=901.901901..-0.901901..=901`

The repeating decimals should cancel out

`\\999x=901`

solve for x

Divide by
`999` both sides

`990x/990=135/990`

`x=(901)/(999)`