Question

How is 0.136¯¯written as a fraction in simplest form? (its a repeating decimal)

Answer 1

the answer is 3/22

Explanation:

im 100% sure

Answer 2

case a) the repeating decimal is 36

Let

`x=0.1363636..`

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

`1,000x=136.3636..`

`10x=1.3636..`

Subtract
`10x` from
`\\1000x`

`1,000x-10x=136.3636..-1.3636..=135`

The repeating decimals should cancel out

`\\990x=135`

solve for x

Divide by
`990` both sides

`990x/990=135/990`

`x=135/990`

Simplify

Divide by
`45` both numerator and denominator

`x=3/22`

therefore

the answer case a) is

The fraction in simplest form is
`3/22`

case b) the repeating decimal is 136

Let

`x=0.136136136...`

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

`1,000x=136.136136...`

Subtract
`x` from
`\\1000x`

`1,000x-x=136.136136...-0.136136...=136`

The repeating decimals should cancel out

`\\999x=136`

solve for x

Divide by
`999` both sides

`999x/999=136/999`

`x=136/999` -----> irreducible

therefore

the answer case b) is

The fraction in simplest form is
`136/999`