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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Solution

A simplified fraction of the form $\frac{p}{q}$ has a terminating decimal expansion if and only if all the prime factors of $q$ are either 2 or 5.
Given: $q = 2^{3} 5^{2}$
As the only prime factors of the denominator are $2$ and $5$ , the decimal expansion will be terminating.

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

Question 1 (vi)
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 number will have a terminating decimal expansion or a non terminating repeating decimal expansion: 232352

A simplified fraction of the form pq has a terminating decimal expansion if and only if all the prime factors of q are either 2 or 5.Given: q=2352As the only prime factors of the denominator are 2 and 5, the decimal expansion will be terminating.

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

A simplified fraction of the form $\frac{p}{q}$ has a terminating decimal expansion if and only if all the prime factors of $q$ are either 2 or 5.
Given: $q = 2^{3} 5^{2}$
As the only prime factors of the denominator are $2$ and $5$ , the decimal expansion will be terminating.