Question

Write this recurring decirnal 0.833333... as a rational number (i.e. fiaction)

Answer 1

`(5)/(6)`

Explanation:

We require 2 equations with the recurring value , 3 , placed after the decimal point.

let x = 0.8333... ( multiply both sides by 10 and 100 )

10x = 8.3333.. → (1)

100x = 83.333... → (2)

subtract (1) from (2) , thus eliminating the recurring value

90x = 75 ( divide both sides by 90 )

x =
`(75)/(90)` =
`(5)/(6)`

the rational fraction is
`(5)/(6)`