Question

Convert 2.16161616 to a rational number in the form of a/b

Answer 1

`(214)/(99)`

Explanation:

We require to create 2 equations with the repeating digits after the decimal point. Then by subtracting them we eliminate the repeating part.

let x = 2.1616.... → (1)) ← multiply both sides by 100

100x = 216.1616..... → (2)

Subtract (1) from (2)

99x = 214 ( divide both sides by 99 )

x =
`(214)/(99)`