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State true or false:
The fraction $\frac{125}{441}$ will have a terminating decimal expansion.
(Solve without the long division method)

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True

False

answer is B.

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Detailed Solution

The given fraction is

\frac{125}{441}

.
The given fraction in its simplest form is,

\frac{125}{441} = \frac{3 \times 5 \times 7}{3 \times 3 \times 7 \times 7}

\Rightarrow \frac{125}{441} = \frac{5}{3 \times 7}

\Rightarrow \frac{125}{441} = \frac{5}{21}

Prime factorization of

21 = 3 \times 7

Observe that 441 cannot be expressed in the form of

2^{m} \times 5^{n}

where m and n are non-negative integers.
Therefore, the given statement is false.
The correct statement would be that the fraction

\frac{125}{441}

has got a non-terminating repeating decimal expansion.
Hence, option 2 is correct.

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