Question

What is 0.16666666666666666 as a fraction?

Answer 1

`(1)/(6)`

Explanation:

We require to create 2 equations with the repeating 6 placed after the decimal point. Then subtracting the equations eliminates the repeating part.

let x = 0.1666....... ( multiply both sides by 10 and 100 )

10x = 1.666...... → (1)

100x = 16.666...... → (2)

Subtract (1) from (2) to eliminate the repeating decimal, thus

90x = 15 ( divide both sides by 90 )

x =
`(15)/(90)` =
`(1)/(6)`

Thus

0.16666......... =
`(1)/(6)`