Is 5/7 a repeating decimal?




Here we will show you how to determine if 5/7 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 5/7 (5 ÷ 7) is repeating or non-repeating.

Here are the steps to determine if 5/7 is a repeating decimal number:

1) Find the denominator of 5/7 in its lowest form.
The greatest common factor (GCF) of 5 and 7 is 1. Convert 5/7 to its simplest form by dividing the numerator and denominator by its GCF:

   
5 ÷ 1
 
   
7 ÷ 1
 
  = 
   
5
 
   
7
 
   

Thus, the denominator of 5/7 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 5/7 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:

5/7
= repeating


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