Without actually performing the long division, state whether the following rational numbers will have terminating decimal expansion or a non-terminating repeating decimal expansion. Also, find the numbers of places of decimals after which the decimal expansion terminates.
$\frac{23}{2^{3} 5^{2}}$

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Solution

clearly ,the prime factorisation of the denominator of $\frac{23}{2^{3} \times 5^{2}}$ is of the form $2^{m} \times 5^{n}$ . so it has terminating decimal expansion which terminates after $m a x (3, 2) = 3$ places of decimals.

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

\frac{23}{2^{3} 5^{2}}

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Without actually performing the long division, state whether $\frac{23}{2^{3} \times 5^{2}}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

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Without actually performing the long division, state whether the following rational numbers will have terminating decimal expansion or a non-terminating repeating decimal expansion. Also, find the numbers of places of decimals after which the decimal expansion terminates.232352

clearly ,the prime factorisation of the denominator of 2323×52 is of the form 2m×5n. so it has terminating decimal expansion which terminates after max(3,2)=3 places of decimals.

Without actually performing the long division, state whether the following rational numbers will have terminating decimal expansion or a non-terminating repeating decimal expansion. Also, find the numbers of places of decimals after which the decimal expansion terminates.
$\frac{23}{2^{3} 5^{2}}$

clearly ,the prime factorisation of the denominator of $\frac{23}{2^{3} \times 5^{2}}$ is of the form $2^{m} \times 5^{n}$ . so it has terminating decimal expansion which terminates after $m a x (3, 2) = 3$ places of decimals.