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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? 43.123456789

Q3 (1)   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? 43.123456789

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\\43.123456789=\frac{43123456789}{10^{9}}\\ 43.123456789=\frac{43123456789}{2^{9}\times 5^{9}}

The denominator is of the form 2a x 5b where a = 9 and b = 9. Therefore the given number is rational and has a terminating decimal expansion.

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