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Real Numbers

Question 3:

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 , what can you say about the prime factor of q?

(i) 43.123456789 (ii) 0.120120012000120000… (iii)

Answer:

(i) 43.123456789

Since this number has a terminating decimal expansion, it is a rational number of the form and q is of the form

i.e., the prime factors of q w...

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