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Q: Are all nonterminating decimals irrational and why?

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Not at all. 0.33333... nonterminating = 1/3 rational 0.66666... nonterminating = 2/3 rational 0.1428571428... nonterminating = 1/7 rational 0.55555... nonterminating = 5/9 rational

Yes

Yes.

No, none of them do.

No because non-repeating decimals may be terminating.But suppose you consider terminating decimals as consisting of repeating 0s. That is, 1/8 = 0.125 = 0.12500....Then all non-repeating decimals are irrational.

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Not at all. 0.33333... nonterminating = 1/3 rational 0.66666... nonterminating = 2/3 rational 0.1428571428... nonterminating = 1/7 rational 0.55555... nonterminating = 5/9 rational

Irrational numbers.

They are irrational.

Yes

Yes.

an irrational number

No, none of them do.

It is an infinite non-repeating decimal which represents an irrational number.

1/3 = 0.333333333...1/7 = 0.142857142857....pi = 3.1415926535...

No. If they are recurring, then they are rational.

No, no repeating decimal is irrational. All repeating decimals can be converted to fractions. They are, however, non-terminating.

No because non-repeating decimals may be terminating.But suppose you consider terminating decimals as consisting of repeating 0s. That is, 1/8 = 0.125 = 0.12500....Then all non-repeating decimals are irrational.

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