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State true or false:
The denominator of 43.123456789 can be expressed in the form of $2^{m} \times 5^{n}$ , after prime factorization.

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True

False

answer is A.

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Detailed Solution

The given number is 43.123456789.

43.123456789 = \frac{43123456789}{10^{9}}

\Rightarrow 43.123456789 = \frac{43123456789}{2^{9} \times 5^{9}}

Thus, it is a terminating decimal number as it's denominator can be expressed in the form of

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

where m and n are non negative integers after prime factorization, having factors in terms of 2 and 5.
Therefore, it is true that the denominator of 43.123456789 can be expressed in the form of

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

, after prime factorization.
Hence, option 1 is correct.

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