Question

Without actually performing the long division, state whether the following rational number will have a terminating decimal expansion or non -terminating decimal expansion

$\frac{15}{1600}$

• A. Terminating decimal expansion
  
• B. Non-terminating decimal expansion
• C. Cannot be determined
• D. None

Answer 1

The correct option is A Terminating decimal expansion

Factorize the denominator we get $1600=2\times 2\times 2\times 2\times 2\times 2\times 5\times 5=2^6\times 5^2$
so denominator is in form of $2^n\times 5^m$
Hence $\frac{15}{1600}$ is terminating.