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Determine whether the following fractions terminate in their decimal form. Show all work and explain your reasoning. YOU CAN NOT USE A CALCULATOR. Try not using long division.

Determine whether the following fractions terminate in their decimal form. Show all-example-1
User Laziale
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1 Answer

2 votes

Answer:

8/22: this fraction will NOT terminate

189/270: this fraction WILL terminate

Explanation:

I saw in the question that it says to solve the question by demonstrating the method discussed in class. I don't know what's the method you were taught, but I'll explain how I solved it.

When a fraction is in its simplest form, write out the prime factors of the denominator. If the denominator has 2s and/or 5s, the fraction WILL terminate in their decimal form.

8/22 in its simplest form is 4/11:

The only prime factors of the denominator, 11, are 1 and 11. There are no 2s and/or 5s present, so this fraction will NOT terminate.

189/270 in its simplest form is 7/10.

The prime factors of 10 are 2 and 5, meaning that this fraction WILL terminate.

Hope it helps (●'◡'●)

User Ddso
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