Question

Question #23724

Answer 1

`27/99 = 3/11`

Explanation:

There is a clever technique to change a recurring decimal into a fraction:

Let `x = 0.27272727.... " 2 recurring digits "`

`100x= 27.27272727...." note that the digits line up"`

`99x = 27.00000000....`

`x = 27/99 = 3/11`

If one digit recurs, multiply by 10.
If two digits recur, multiply by 100.
If three digits recur, multiply by 1,000, and so on.