How do you convert 0.789 (789 repeating) to a fraction?
This is written as
Do some algebra and reasoning to find
The process for converting repeating decimals to fractions is confusing at first, but with practice it's pretty easy.
You begin by setting
Then, multiply the equation by
We do this so we can move one chunk of the repeating part to the left of the decimal point. This sets us up for the next, most important step: subtracting
On the left side of the equation, this is simply
And take a good look at this subtraction problem:
The right side of the equation becomes
To solve for