Question

Prove algebraically that 0.5 recurring = 5/9

write your proof in the box, below, and use x in the working. The concluding line has been written for you.#

Therefore x = 5/9

Answer 1

see explanation

Explanation:

We require 2 equations with the recurring part after the decimal point.

Let x = 0.555..... → (1)

Multiply both sides by 10, then

10x = 5.555..... → (2)

Subtract (1) from (2) thus eliminating the recurring decimal

(10x - x) = (5.5555 - 0.5555 ), that is

9x = 5 ( divide both sides by 9 )

x =
`(5)/(9)`