Without actually performing the long deviation, state whether the following rational number will have a terminating decimal expansion or a non-terminating repeating decimal expansion:
$\frac{15}{1600}$

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Solution

$\begin{matrix} \frac{15}{1600} = \frac{15}{2^{6} \times 5^{2}} \end{matrix}$

Since prime factorization of the denominator is of the form $2^{n} 5^{m}$ where m,n are whole numbers
therefore it has terminating decimal.

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Without actually performing the long deviation, state whether the following rational number will have a terminating decimal expansion or a non-terminating repeating decimal expansion:151600

151600=1526×52Since prime factorization of the denominator is of the form 2n5m where m,n are whole numberstherefore it has terminating decimal.

Without actually performing the long deviation, state whether the following rational number will have a terminating decimal expansion or a non-terminating repeating decimal expansion:
$\frac{15}{1600}$

$\begin{matrix} \frac{15}{1600} = \frac{15}{2^{6} \times 5^{2}} \end{matrix}$

Since prime factorization of the denominator is of the form $2^{n} 5^{m}$ where m,n are whole numbers
therefore it has terminating decimal.