Question

How is 0.136¯ written as a fraction in simplest form? Enter your answer in the box.

Answer 1

The answer is 3/22
I see the answer 17/125 around a lot, and that's not wrong but I don't think it's simplified enough

Answer 2

`0.13\bar{6}` as fraction
`(41)/(300)`

Explanation:

We are given a repeating decimal number.

`0.13\bar{6}`

We need to change into fraction.

Repeating decimal means number repeat infinite number of times.

So, we can write
`0.13\bar{6}` = 0.1366666666..............

Let,

`x=0.1366666666.......`

Multiply both sides by 100

`100x=13.66666666.......-------------(1)`

Multiply both sides by 10

`1000x=136.66666666......-------------(2)`

Subtract eq(2) - eq(1)

`1000x-100x=136.666666.... - 13.666666....`

`900x=123`

`x=(123)/(900)=(41)/(300)`

Hence,
`0.13\bar{6}` as fraction
`(41)/(300)`