Question

For any natural number n > 1, write the infinite decimal expansion of 1/n (for example, we write 1/2 = bar 0.49 as its infinite decimal expansion, not 0.5). Determine the 4 length of the non-periodic part of the (infinite) decimal expansion of 1/n.

Answer 1

Hence 10^k = 2^k.5^k => k is higher of the two exponents of 2 5 in prime factorization of n.

=> k = maximum {exponent of 2, exponent of 5}