Devi takes a fraction whose denominator (in lowest terms) is N. She finds N has the prime factorisation N = 2^2 × 5 × 7. She wants the SMALLEST whole number she can multiply N by so that the new denominator gives a terminating decimal (only 2s and 5s). What is that multiplier? (Assume the factor 7 cannot cancel with the numerator.)

Question

Accepted Answer

It is impossible while 7 remains in lowest terms. Multiplying the denominator by any number cannot remove the factor 7 (it only adds primes). As long as 7 is in the denominator in lowest terms, the decimal stays non-terminating recurring. So no multiplier makes it terminate.

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