Repeating or Terminating Decimal Number

harpazo

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A rational number is defined as the quotient of two integers. When written as a decimal, the decimal will either repeat or terminate. By looking at the denominator of the rational number, there is a way to tell in advance whether its decimal representation will repeat or terminate. How is this done without getting too technical?
 
A fraction, reduced to lowest terms, will correspond to a terminating decimal if and only if the prime factorization of the denominator has only powers of 2 and 5. If there are any other factors it will be an infinitely repeating decimal.
 
… without getting too technical?
If you'd like information about prime factorization, here is an explanation. The following serve as basic examples to go with Halls' explanation.

The decimal form of 7/20 terminates; the prime factorization of 20 is 22×5

The decimal form of 7/30 repeats; the prime factorization of 30 is 2×3×5

?
 
If you'd like information about prime factorization, here is an explanation. The following serve as basic examples to go with Halls' explanation.

The decimal form of 7/20 terminates; the prime factorization of 20 is 22×5

The decimal form of 7/30 repeats; the prime factorization of 30 is 2×3×5

?

Nice explanation. Can you please provide at least two more examples?
 
Last edited:
Nice explanation. Can you please provide at least two more examples?
? If you understand prime factorizations, then you can create at least two more examples and post them. Use the explanation Halls provided in post #2.

Otherwise, do you have a specific question?

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? If you understand prime factorizations, then you can create at least two more examples and post them. Use the explanation Halls provided in post #2.

Otherwise, do you have a specific question?

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This is it for tonight. More math tomorrow morning.
 
I'll wait to see whether that means you'll answer the question.

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Tomorrow morning new questions will be posted from R.2, specific math questions, you know, with work shown.
 
Do you have another question in this thread? Why are you asking for more examples?

:confused:
 
Probably because he wants you to do the work for him, and if you don't he'll move on to a new problem. That's been his pattern for a long while now.

-Dan
 
Probably because he wants you to do the work for him, and if you don't he'll move on to a new problem. That's been his pattern for a long while now.

-Dan

I requested two more samples for my personal math files. I not only read each reply. I also save what I think is important for me to know for further study. Nothing more, nothing less.
 
Well, then, go ahead and follow the advice in post #5. It'll help you get the idea in your mind more firmly. It's one thing to understanding a process but another to actually use that framework for yourself. It's working with the framework on new problems that actually instructs you.

-Dan
 
Well, then, go ahead and follow the advice in post #5. It'll help you get the idea in your mind more firmly. It's one thing to understanding a process but another to actually use that framework for yourself. It's working with the framework on new problems that actually instructs you.

-Dan

Thank you, Dan.
 
I told you, in the first response to your question, that "A fraction, reduced to lowest terms, will correspond to a terminating decimal if and only if the prime factorization of the denominator has only powers of 2 and 5. If there are any other factors it will be an infinitely repeating decimal."

Now, do you know what "prime numbers" are? Do you know how to "factor" a number? Do you know what "prime factorization" means? If you know those fairly basic things then you should be able to create your own examples. Try it and post a few here.
 
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