Write the following as a fraction and show your work. 0.83 (the three is repeating) I don't know how to do it with only one of the numbers repeating and it is not in my book.

Answer 1

Here is a neat algorithm to change any repeating decimal into an exact fraction

Assume you have only the decimal portion of your number, ie, for 4.5676767... consider only the 5676767..

For the numerator, write down all the digits to the end of your repeat, subtract from that the part that does not repeat.

For the denominator, write down a 9 for each digit in the repeating loop, followed by the number of digits that don't repeat.

e.g. 0.45676767..
=(4567-45)/9900
=4522/9900, now reduce to
2261/9900

your number would be
.833333. = (83-8)/90
= 75/90
= 5/6