Choose whether the statement is true or false: $\frac{43}{3^{4} \times 4^{2}}$ is a terminating decimal number.

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True

False

answer is B.

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Detailed Solution

Here, we are given numbers as

\frac{43}{3^{4} \times 4^{2}}

Now, the denominator of this number is expressed in prime factors and we have to evaluate when the number will terminate in its decimal expansion. For this, let us understand the concept of terminating decimals. If the prime factorization of the denominator of a fraction has only factors of 2 and factors of 5, the decimal expansion terminates.
If there is a prime factor in the denominator other than 2 or 5, then the decimal expansion repeats. Now, let us observe the denominator of the given number. It has prime factors of 3 and 5. Since it has prime factors other than 2 or 5, this decimal expansion will repeat. Hence, the decimal expansion of