Question

What is the value of .36 REPEATING written as a fraction ??????

Answer 1

Turns out that `0.bar(36)` is equivalent to `4/11`

Explanation:

So, I totally cheated and used my TI-83 plus to get the answer, but lets try to figure out a way to do the conversion by hand:

When you have a repeating decimal, you can write it as a fraction where the numerator is the repeating pattern, but written as an integer, and the denominator is made up of repeating nines and is the same length as the repeating number set.

For our purposes, we have two digits in the set, and therefore its divisible by 99

`0.bar(36)=36/99`

Now we can simplify. The largest common factor between the numerator and denominator is 9, so we can pull that out:

`36/99=cancel(9/9)xx4/11`

Now, we have our fully reduced and converted fraction:

`color(green)(0.bar(36)=4/11`