Is 13/75 a repeating decimal?

Here we will show you how to determine if 13/75 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 13/75 (13 ÷ 75) is repeating or non-repeating.

Here are the steps to determine if 13/75 is a repeating decimal number:

1) Find the denominator of 13/75 in its lowest form.
The greatest common factor (GCF) of 13 and 75 is 1. Convert 13/75 to its simplest form by dividing the numerator and denominator by its GCF:

		13 ÷ 1
		75 ÷ 1

		13
		75

Thus, the denominator of 13/75 in its lowest form is 75.

2) Find the prime factors of the answer in Step 1.
The prime factors of 75 are all the prime numbers that you multiply together to get 75. The prime factors of 75 are:

3 x 5 x 5

3) Determine if 13/75 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:

13/75
= repeating

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