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A rational number in its decimal expansion is $327.7081$ . What are the prime factor of $q$ when this number is expressed in the form $\frac{p}{q}$ ?

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2 and 5

3 and 7

2 and 8

3 and 5

answer is A.

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Detailed Solution

Given decimal number is

327.7081

327.7081

is the terminating decimal number.

327.7081

is a rational number and its denominator must have the form

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

.
Then 327.7081 can be written as,

⇒ 327.7081 b = 327708110000 ⇒ b = 3277081 2 × 2 × 2 × 1250 ⇒ b = 3277081 2 × 2 × 2 × 2 × 625 ⇒ b = 3277081 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5

\Rightarrow b = \frac{3277081}{2^{4} \times 5^{4}}

\Rightarrow b = \frac{3277081}{{(2 \times 5)}^{4}}

The prime factors of the denominator of the decimal expression 327.7081 are 2 and 5.
Hence, option 1 is correct.

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