Question

Convert the decimal expansion 0.291666... to a fraction

Answer 1

Answer: $\frac{7}{24}$

Step-by-step 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

$10x-x=2.9166...-0.29166...\\\Rightarrow9x=2.625\\\Rightarrow\ x=\frac{2.625}{9}=\frac{2625}{1000}$

Simplify it to the lowest fraction, we get

$x=\frac{7}{24}$

Answer 2

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.