Is 13/65 a repeating decimal?




Here we will show you how to determine if 13/65 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 13/65 (13 ÷ 65) is repeating or non-repeating.

Here are the steps to determine if 13/65 is a repeating decimal number:

1) Find the denominator of 13/65 in its lowest form.
The greatest common factor (GCF) of 13 and 65 is 13. Convert 13/65 to its simplest form by dividing the numerator and denominator by its GCF:

   
13 ÷ 13
 
   
65 ÷ 13
 
  = 
   
1
 
   
5
 
   

Thus, the denominator of 13/65 in its lowest form is 5.

2) Find the prime factors of the answer in Step 1.
The prime factors of 5 are all the prime numbers that you multiply together to get 5. The prime factors of 5 are:

5

3) Determine if 13/65 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 not the case here, which means that our answer is as follows:

13/65
= non-repeating


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