Question

Write the recurring decimal 0.473737373... as a fraction.​

Answer 1

`(469)/(990)`

Explanation:

We require 2 equations with the repeating digits after the decimal point.

By subtracting the 2 equations eliminates the repeating digits.

let x = 0.47373737.....

Multiply both sides by 100 and 10000, that is

100x = 47.3737... → (1)

10000x = 4737.3737.... → (2)

Subtract (1) from (2)

9900x = 4690 ( divide both sides by 9900 )

x =
`(4690)/(9900)` =
`(460)/(990)` ← in simplest form