Is 7/21 a repeating decimal?

Here we will show you how to determine if 7/21 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 7/21 (7 ÷ 21) is repeating or non-repeating.

Here are the steps to determine if 7/21 is a repeating decimal number:

1) Find the denominator of 7/21 in its lowest form.
The greatest common factor (GCF) of 7 and 21 is 7. Convert 7/21 to its simplest form by dividing the numerator and denominator by its GCF:

		7 ÷ 7
		21 ÷ 7

		1
		3

Thus, the denominator of 7/21 in its lowest form is 3.

2) Find the prime factors of the answer in Step 1.
The prime factors of 3 are all the prime numbers that you multiply together to get 3. The prime factors of 3 are:

3

3) Determine if 7/21 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:

7/21
= repeating

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