Is 7/46 a terminating decimal?




Here we will show you how to determine if 7/46 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 7/46 (7 ÷ 46) is terminating or non-terminating.

Here are the steps to determine if 7/46 is a terminating decimal number:

1) Find the denominator of 7/46 in its lowest form.
The greatest common factor (GCF) of 7 and 46 is 1. Convert 7/46 to its simplest form by dividing the numerator and denominator by its GCF:

   
7 ÷ 1
 
   
46 ÷ 1
 
  = 
   
7
 
   
46
 
   

Thus, the denominator of 7/46 in its lowest form is 46.

2) Find the prime factors of the answer in Step 1.
The prime factors of 46 are all the prime numbers that you multiply together to get 46. The prime factors of 46 are:

2 x 23

3) Determine if 7/46 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:

7/46
= non-terminating


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