Question

Convert the decimal expansion 0.291666... to a fraction

Answer 1

7/24
You could try rounding up to 0.292 first and try guessing it it gets to 73/250 which you could guess into 70/240.

Answer 2

Answer:
`(7)/(24)`

Explanation:

The given decimal expansion : 0.291666......, where 6 is repeating.

Let
`x=0.291666...` (1)

First we multiply 10 on the both sides, we get

`10x=2.916666......` (2)

Now, subtract (1) from (2), we get

`10x-x=2.9166...-0.29166...\\\Rightarrow9x=2.625\\\Rightarrow\ x=(2.625)/(9)=(2625)/(1000)`

Simplify it to the lowest fraction, we get

`x=(7)/(24)`