Question

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.

Answer 1

327.7081 is terminating decimal number.

So, it represents a rational number and also its denominator must have the form 2^m × 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.