Is 4/7 a terminating decimal?




Here we will show you how to determine if 4/7 is a terminating decimal or a non-terminating decimal.

A terminating decimal is a decimal number that has a finite number of decimals and does not go on indefinitely. We want to know if the decimal number you get when you divide the fraction 4/7 (4 ÷ 7) is terminating or non-terminating.

Here are the steps to determine if 4/7 is a terminating decimal number:

1) Find the denominator of 4/7 in its lowest form.
The greatest common factor (GCF) of 4 and 7 is 1. Convert 4/7 to its simplest form by dividing the numerator and denominator by its GCF:

   
4 ÷ 1
 
   
7 ÷ 1
 
  = 
   
4
 
   
7
 
   

Thus, the denominator of 4/7 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 4/7 is terminating
A fraction is a terminating decimal if the prime factors of the denominator of the fraction in its lowest form only contain 2s and/or 5s or no prime factors at all. This is not the case here, which means that our answer is as follows:

4/7
= non-terminating


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