Question

Express each of the following repeating decimals as a quotient of integers 0.57 bar on 57​

Answer 1

`(19)/(33)`

Explanation:

the bar on 57 means that the digits 57 are repeated.

we require 2 equations with the repeating digits placed after the decimal point.

let x = 0.5757... (1) ← multiply both sides by 100

100x = 57.5757... (2)

subtract (1) from (2) thus eliminating the repeating digits

99x = 57 ( divide both sides by 99 )

x =
`(57)/(99)` =
`(19)/(33\\)`