How do you convert 0.363636363 (recurring) to a mixed number. Give answer in its simplest form??? Thanks a lot

Answer 1

Whenever you have a repeating part, put it over the equivalent number of 9s. For example, you have 36 repeating (two digit repeat). So the equivalent fraction would be:
36/99

But you can reduce this by dividing top and bottom by 9 to get:
4/11

To double-check, put 4/11 into your calculator.

Answer 2

Hi there.

If a recurring decimal has two digits in the recurring pattern (and no other digits following the decimal point), then the two digit number created by these gives the number of 99ths that the decimal number represents.

Since the digits here are 3 & 6, that means the number represented is 36/99. This fraction can now be simplified since each part is divisible by 9; this leaves us with 4/11.

And there's your final answer .... 4/11.

I hope this helps, but do please feel free to drop me a line if you'd like to go over this or any aspect of figure-work further.

Answer 3

let x = 0.363636363.........
=> 100 x = 36.363636363
........... x= 0.363636363
=> 99x = 36
=> x = 36/99
=> x = 4/11

QED

Answer 4

0.36 with a line up on .36