Question

Write these recurring decimals as fractions:

1. 0.7 recurring
2. 0.7235 [the 3 and 5 are recurring]

Answer 1

`(7)/(9)` and
`(7163)/(9900)`

Explanation:

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

(1)

let x = 0.777... (1) ← multiply both sides by 10

10x = 7.777... (2)

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

9x = 7 ( divide both sides by 9 )

x =
`(7)/(9)`

(2)

let x = 0.723535.. ( multiply both sides by 100 and 10,000 )

100x = 72.3535.... (1)

10,000x = 7235.3535..... (2)

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

9900x = 7163 ( divide both sides by 9900 )

x =
`(7163)/(9900)`