Question

How do you turn 1.83 (3 repeating) into a simplified fraction?

Answer 1

The value of 1.83.... (3 repeating) in the form of a simplified fraction =
`(165)/(90)`

Explanation:

Let x be = 1.83....(3 repeating)

∵ only one number is repeating, multiply the number with 10

∴ 10x = 10 × 1.83.... = 18.3..... (3 repeating)

Subtracting both the equations = 10x - x = 18.3.... - 1.83....

= 9x = 16.5

∴ x =
`(16.5)/(9)` =

`(16.5)/(9)` × 10 =
`(165)/(90)`