Is 3/21 a repeating decimal?

Here we will show you how to determine if 3/21 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 3/21 (3 ÷ 21) is repeating or non-repeating.

Here are the steps to determine if 3/21 is a repeating decimal number:

1) Find the denominator of 3/21 in its lowest form.
The greatest common factor (GCF) of 3 and 21 is 3. Convert 3/21 to its simplest form by dividing the numerator and denominator by its GCF:

		3 ÷ 3
		21 ÷ 3

		1
		7

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

2) Find the prime factors of the answer in Step 1.
The prime factors of 7 are all the prime numbers that you multiply together to get 7. The prime factors of 7 are:

7

3) Determine if 3/21 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:

3/21
= repeating

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