How you express recuring decimals in fractional form?

Answer 1

There is a trick to doing this.
Let's take an easy example first and work though it. Then a slightly harder one. It is easier to show how it is done that to explain how to do it.

So look at .1 repeating.

let x=.1 repeating, I will write .111...since answers.com does not have a way to place the bar over the 1.

The ... means it goes on forever.

now 10x=1.111...

If I subtract x I can get rid of the .111... part and be left with just 1
so 9x=1 and
x=1/9

We can use the same technique with something like .75.75...

Let x=.7575757575...

Now if we multiply by 100 this time instead of 10 we take care of the two numbers that repeat.
So 100x=75.75757575...

99x=75
and x=75/99

This idea can be extended to any other recurring decimal.