Question

Convert this repeating decimal to a fraction: 0.75757575....

Answer 1

`(25)/(33)`

Explanation:

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

let x = 0.7575..... (1) ← multiply both sides by 100

100x = 75.7575... (2)

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

99x = 75 ( divide both sides by 99 )

x =
`(75)/(99)` =
`(25)/(33)` ← in simplest form

Answer 2

25/33

Explanation: