Question

A rational no 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 of pq ? Give Reasons.

Answer 1

If the factors of denominator of the given rational number is of form 2ⁿ 5^m ,where n and m are non negative integers, then the decimal expansion of the rational number is terminating otherwise non terminating recurring.
We know that a rational number has either terminating or non terminating repeating decimal expansion.

SOLUTION:
Here, 327.7081 has terminating decimal expansion so it represents a rational number.
327.7081= 3277081/10000= p/q
Thus q=10⁴ , whose factors are 2⁴ × 5⁴.

HOPE THIS WILL HELP YOU....

Answer 2

Hey ! Here's your answer.

In the form p/q it can be written as 3277081/10000.

so,the prime factors of 10000=
2×2×2×2×5×5×5×5.

Thanks :)