Question

10. 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 ? Give reasons.

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Answer 1

Answer:

The answer is .........

We know that The rational no having denominator 3, 7, 9, 11, 13, 17, 23, 27.............. and multiple of these number will have non terminating decimal .

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As  decimal expansion is 327.7081 which is terminating.

prime factors of q, when this number is expressed in the form p/q will not be above number, it will be 2 or 5 or both.

Answer 2

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....