Mathematics

Problem

State the nature of the decimal expansion of a rational number

\frac{p}{q}

, expressed in simplest form, if the prime factorisation of

q

2^m5^n

for some non-negative integers

m,n

. a) Non-terminating recurring b) Terminating c) Terminating only if

m=n

, otherwise non-terminating recurring d) Terminating if either

m

n

0

, otherwise non-terminating recurring