Convert .83 (the Three Is Repeating) To A Fraction & Show Work?

The solution is as follows;

You have number 0.833333.... This number is equal to some fraction; call this fraction "x". That is:

X = 0.833333...

There is one repeating digit in this decimal, so multiply x by "1" followed by one zero; that is, multiply by 10:

10x = 8.33333....

Now subtract the former from the latter:

10x=8.33333
x = 0.833333
------
9x = 7.50000

That is, 9x = 7.5 = 75/10 = 15/2. Solving this, we get x = 15/18. (You can verify this by plugging "15 ÷ 18" into your calculator and seeing that you get "0.833333..." for an answer.)
thanked the writer.
Anonymous commented
It's 5/6 ....that gets you .833333... As well. And it's simplified
Here's how to convert .83 to a fraction...

There is not much that can be done to figure out how to write .83 as a fraction, except to literally use what the decimal portion of your number, the .83, means.
Since there are 2 digits in 83, the very last digit is the "100th" decimal place.

So we can just say that .83 is the same as 83/100.

So your final answer is: .83 can be written as the fraction
www.webmath.com
thanked the writer. 