Is 24/84 a terminating decimal?

Here we will show you how to determine if 24/84 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 24/84 (24 ÷ 84) is terminating or non-terminating.

Here are the steps to determine if 24/84 is a terminating decimal number:

1) Find the denominator of 24/84 in its lowest form.
The greatest common factor (GCF) of 24 and 84 is 12. Convert 24/84 to its simplest form by dividing the numerator and denominator by its GCF:

		24 ÷ 12
		84 ÷ 12

		2
		7

Thus, the denominator of 24/84 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 24/84 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:

24/84
= non-terminating

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