Question

What is 0.3111111111111111 as a fraction?

Answer 1

`\sf~N=0.3\overline{1}`

There is only one repeating number, so we multiply both sides by
`\sf10^1` or
`\sf10`.


`\sf10N=3.\overline{1}`

Now subtract the original number we had to both sides, which is the same as
`\sf~1N` or
`\sf~N`

So we have:


`\sf9N=2.8`

Divide 9 to both sides:


`\sf~N=(2.8)/(9)`

Multiply the fraction by 10 to get rid of the decimal in the numerator.


`\sf~N=(28)/(90)`

Simplify the fraction by dividing the numerator and denominator by 2:


`\sf~N=\boxed{\sf(14)/(45)}`