Is 5/30 a terminating decimal?

Here we will show you how to determine if 5/30 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 5/30 (5 ÷ 30) is terminating or non-terminating.

Here are the steps to determine if 5/30 is a terminating decimal number:

1) Find the denominator of 5/30 in its lowest form.
The greatest common factor (GCF) of 5 and 30 is 5. Convert 5/30 to its simplest form by dividing the numerator and denominator by its GCF:

		5 ÷ 5
		30 ÷ 5

		1
		6

Thus, the denominator of 5/30 in its lowest form is 6.

2) Find the prime factors of the answer in Step 1.
The prime factors of 6 are all the prime numbers that you multiply together to get 6. The prime factors of 6 are:

2 x 3

3) Determine if 5/30 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:

5/30
= non-terminating

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