Is 4/33 a repeating decimal?

Here we will show you how to determine if 4/33 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 4/33 (4 ÷ 33) is repeating or non-repeating.

Here are the steps to determine if 4/33 is a repeating decimal number:

1) Find the denominator of 4/33 in its lowest form.
The greatest common factor (GCF) of 4 and 33 is 1. Convert 4/33 to its simplest form by dividing the numerator and denominator by its GCF:

		4 ÷ 1
		33 ÷ 1

		4
		33

Thus, the denominator of 4/33 in its lowest form is 33.

2) Find the prime factors of the answer in Step 1.
The prime factors of 33 are all the prime numbers that you multiply together to get 33. The prime factors of 33 are:

3 x 11

3) Determine if 4/33 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:

4/33
= repeating

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