Is 2/3 a repeating decimal? Here we will show you how to determine if 2/3 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 2/3 (2 ÷ 3) is repeating or non-repeating.

Here are the steps to determine if 2/3 is a repeating decimal number:

1) Find the denominator of 2/3 in its lowest form.
The greatest common factor (GCF) of 2 and 3 is 1. Convert 2/3 to its simplest form by dividing the numerator and denominator by its GCF:

 2 ÷ 1 3 ÷ 1
=
 2 3

Thus, the denominator of 2/3 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 2/3 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:

2/3
= repeating

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