Question

(2CQ) Write the repeating decimal as a fraction .15

Answer 1

c.
`(5)/(33)`

Explanation:

The given decimal is
`0.\bar {15}`

Let
`y=0.\bar {15}...(1)`

Multiply equation (1) by 100.

`100y=15.\bar {15}...(2)`

Subtract equation (1) from equation (2)

`\Rightarrow 100y-y=15.\bar {15}-0.\bar {15}`

`\Rightarrow 99y=15`

Divide both sides by 99.

`\Rightarrow y=(15)/(99)`

Simplify;

`\Rightarrow y=(5)/(33)`