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प्रश्न
A rational number in its decimal expansion is 327.7081. What can you say about the prime factors of q, when this number is expressed in the form `p/q`? Given reasons.
उत्तर
327.7081 is terminating decimal number.
So, it represents a rational number and also its denominator must have the form 2m × 5n.
Thus, 327.7081 = `3277081/10000 = p/q`
∴ q = 104
= 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5
= 24 × 54
= (2 × 5)4
Hence, the prime factors of q is 2 and 5.
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