Question

Write Your recurrring decimal 0.255555...... as a fraction

Answer 1

`(23)/(90)`

Explanation:

we require 2 equations with the recurring digit placed after the decimal point.

let x = 0.2555.. ( multiply both sides by 10 and 100 )

10x = 2.555... (1)

100x = 25.555.... (2)

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

90x = 23 ( divide both sides by 90 )

x =
`(23)/(90)`

Answer 2

`\sf (23)/(90)`

Explanation:

x = 0.25555..... --------------(I)

Number of non-recurring digits is 1. So, multiply equation (I) by 10.

10x = 2.5555.... --------------(II)

Number of recurring digits is 1. So, multiply equation (II) by 10.

100x = 25.5555...... (III)

Subtract equation (II) from (III)

100x = 25.5555........

10x = 2.5555.......

- -

90x = 23

x = 23/90