Write the recurring decimal 0,101010101... . as a fraction in its simplest form.

Question

asked Nov 9, 2021 157k views

2 Answers

Troyen · Answer 1 · 2021-11-10T09:54:20+0000

Answer:

(10)/(99)

Explanation:

We require to create 2 equations with the repeating decimal after the decimal point.

let x = 0.10101.... → (1)

Multiply both sides by 100

100x = 10.10101.... → (2)

Subtracting (1) from (2) eliminates the repeating decimal, thus

99x = 10 ( divide both sides by 99 )

x =
(10)/(99)