Is 30/4 a terminating decimal?

Here we will show you how to determine if 30/4 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 30/4 (30 ÷ 4) is terminating or non-terminating.

Here are the steps to determine if 30/4 is a terminating decimal number:

1) Find the denominator of 30/4 in its lowest form.
The greatest common factor (GCF) of 30 and 4 is 2. Convert 30/4 to its simplest form by dividing the numerator and denominator by its GCF:

		30 ÷ 2
		4 ÷ 2

		15
		2

Thus, the denominator of 30/4 in its lowest form is 2.

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

2

3) Determine if 30/4 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 the case here, which means that our answer is as follows:

30/4
= terminating

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