Is 19/38 a repeating decimal?

Here we will show you how to determine if 19/38 is a repeating decimal or a non-repeating decimal.

A repeating decimal is a decimal number that goes on forever. We want to know if the decimal number you get when you divide the fraction 19/38 (19 ÷ 38) is repeating or non-repeating.

Here are the steps to determine if 19/38 is a repeating decimal number:

1) Find the denominator of 19/38 in its lowest form.
The greatest common factor (GCF) of 19 and 38 is 19. Convert 19/38 to its simplest form by dividing the numerator and denominator by its GCF:

		19 ÷ 19
		38 ÷ 19

		1
		2

Thus, the denominator of 19/38 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 19/38 is repeating
A fraction is a repeating decimal if the prime factors of the denominator of the fraction in its lowest form do not only contain 2s and/or 5s or do not have any prime factors at all. This is not the case here, which means that our answer is as follows:

19/38
= non-repeating

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