Is 3/27 a terminating decimal?

Here we will show you how to determine if 3/27 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 3/27 (3 ÷ 27) is terminating or non-terminating.

Here are the steps to determine if 3/27 is a terminating decimal number:

1) Find the denominator of 3/27 in its lowest form.
The greatest common factor (GCF) of 3 and 27 is 3. Convert 3/27 to its simplest form by dividing the numerator and denominator by its GCF:

		3 ÷ 3
		27 ÷ 3

		1
		9

Thus, the denominator of 3/27 in its lowest form is 9.

2) Find the prime factors of the answer in Step 1.
The prime factors of 9 are all the prime numbers that you multiply together to get 9. The prime factors of 9 are:

3 x 3

3) Determine if 3/27 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:

3/27
= non-terminating

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