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Show that each of the following numbers ...

Show that each of the following numbers is rational. What can you say about the prime factors of their denominators ?
(i) 23.123456789 (ii) 32. `overline(123456789)`

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(i) Clearly , the given number 23.123456789 is a terminationg decimal. So, it is rational and the prime factors of its denominatior are 2 or 5 or both.
(ii) Clearly, the given number 32. `overline(123456789)` is a nonterminating repeating decimal. So, it is rational and the prime factors of its denominator are other than 2 or 5 also.
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