Question

a rational no. in its decimal expansion is 327.7081. what can you say about the prime factors of q, when this no. is expressed in the form p/q ? give reasons​

Answer 1

Answer:

327.7081 can be expressed as 3277081/10000. In p/q format.

and for q=10000 it's factors are.

2 × 5000.

4 × 2500

5 × 2000

8 × 1250

10 × 1000

16 × 625

20 × 500

25 × 400

40 × 250

50 × 200

80 × 125

100 × 100

and of which prime no.s or prime factors are only 2 and 5

Answer 2

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Since, 327.7081 has a terminating decimal expansion its denominator should be of the form 2^m x 5^n, where m, n are non-negative integers.

Further,

327.7081 can be expressed as

3277081/10000 = p/q

⇒ q = 10000 = 23 x 53

Hence, the prime factors of q has only factors of 2 and 5.

Thank you!!

@itzshivani