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

Question

asked Nov 28, 2023 169k views

2 Answers

Michael Ros · Answer 1 · 2023-11-30T09:50:31+0000

Answer:

(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