Is 75/90 a repeating decimal?

Here we will show you how to determine if 75/90 is a repeating decimal or a non-repeating decimal.

A repeating decimal is a decimal number that goes on forever. We want to know if the decimal number you get when you divide the fraction 75/90 (75 ÷ 90) is repeating or non-repeating.

Here are the steps to determine if 75/90 is a repeating decimal number:

1) Find the denominator of 75/90 in its lowest form.
The greatest common factor (GCF) of 75 and 90 is 15. Convert 75/90 to its simplest form by dividing the numerator and denominator by its GCF:

		75 ÷ 15
		90 ÷ 15

		5
		6

Thus, the denominator of 75/90 in its lowest form is 6.

2) Find the prime factors of the answer in Step 1.
The prime factors of 6 are all the prime numbers that you multiply together to get 6. The prime factors of 6 are:

2 x 3

3) Determine if 75/90 is repeating
A fraction is a repeating decimal if the prime factors of the denominator of the fraction in its lowest form do not only contain 2s and/or 5s or do not have any prime factors at all. This is the case here, which means that our answer is as follows:

75/90
= repeating

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