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Real Numbers

Question

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The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form , p q what can you say about the prime factors of q?

(ii) 0.120120012000120000. .

Solution

(ii) Clearly, 0.120120012000120000 ... is a non-terminating and non-repeating decimal and therefore, it is irrational.

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