If ( \frac{p}{q} ) is in simplest form and (q=2^4\times5^9), what is the maximum number of decimal places in the terminating decimal?

(9)

For a denominator of \\(2^4\times5^9\\), the powers of 2 and 5 must be balanced to form a power of 10. There are only four factors of 2 but nine factors of 5, so multiply by \\(2^5\\) to obtain \\(2^9\times5^9=10^9\\). Therefore a terminating decimal can have at most nine decimal places.

The rule is that the maximum number of places is the larger of the exponents of 2 and 5 in the simplified denominator. Here, \\(\max(4,9)=9\\), so option C is correct. The exponents should not be added to get 13, because the factors are paired to make tens, with each pair of 2 and 5 producing one factor of 10.

This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Decimal representation.