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Question -

The following real numbers have decimalexpansions as given below. In each case, decide whether they are rational ornot. If they are rational, and of the form, p q what can you say about theprime factors of q?

(i) 43.123456789

(ii) 0.120120012000120000. . .



Answer -

(i) 43.123456789

Since it has a terminating decimal expansion,it is a rational number in the form of p/q and q has factors of 2 and 5 only.

(ii) 0.120120012000120000. . .

Since, it has non-terminating and non-repeating decimal expansion, it is an irrational number.

Since it has non-terminating but repeatingdecimal expansion, it is a rational number in the form of p/q and q has factorsother than 2 and 5.

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