The correct option is B TerminatingThe given fraction, 23/2^35^2 has its denominator composed of only 2 's and 5 's only.Since the fraction is ...

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Check If a Given Rational No. Is Terminating or Not

23/2352

Question

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

Terminating

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Non-terminating

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Ambiguous

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Data insufficient

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Solution

The correct option is B Terminating
The given fraction, $\frac{23}{2^{3} 5^{2}}$ has its denominator composed of only $2$ 's and $5$ 's only.
Since the fraction is in the form of $2^{m} \times 5^{n}$ where ( $n = 3, m = 2$ ),
the rational number $\frac{23}{2^{3} 5^{2}}$ will have a terminating decimal expansion.

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Similar questions

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}}

Q. The decimal expansion of the rational number

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

, will terminate after how many places of decimal?

Question 2
Write down the decimal expansions of
(i) $\frac{13}{3125}$
(ii) $\frac{17}{8}$
(iii) $\frac{15}{1600}$
(iv) $\frac{23}{2^{3} 5^{2}}$
(v) $\frac{6}{15}$
(vi) $\frac{35}{50}$

Express 2352 in exponential form.

Q. Write down the decimal expansions of the rational numbers which have terminating decimal expansions.
(i)

\frac{13}{3125}

(ii)

\frac{17}{8}

(iii)

\frac{15}{1600}

(iv)

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

(v)

\frac{6}{15}

(vi)

\frac{35}{50}

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232352

The correct option is B TerminatingThe given fraction, 232352 has its denominator composed of only 2's and 5's only.Since the fraction is in the form of 2m×5n where (n=3,m=2),the rational number 232352 will have a terminating decimal expansion.

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