Question

 A rational number in its decimal expansion is 327.7081. What would be the prime factors of q when the number is expressed in the p/q form?

(A) 2 and 3                                         

(B) 3 and 5

(C) 2, 3 and 5                                     

(D) 2 and 5​

Answer 1

ANSWER:

(D) 2 AND 5

EXPLANATION:

THIS CAN BE EXPLAINED AS,

327.7081=3277081/10000=p/q

:.q =10000 = 10⁴

= (2x5)⁴= 2⁴ x 5⁴

Answer 2

QUESTION -

A rational number in its decimal expansion is 327.7081. What would be the prime factors of q when the number is expressed in the p/q form?

ANSWER -

If x is a rational number with terminating decimal expansion, then it can be expressed in theform,

p/q,

where p and q are co-prime (the HCF ofpandqis 1) and the prime factorisation ofqis of the form2^n5^m, wherenandmare non-negative integers.

Here 327.7081 is a terminating decimal.

Also 327.7081 = 3277081/10000

= 3277081 / 10^4

= 3277081 / (2 x 5)^4

= 3277081 / 2^4 x 5^4

Hence,

OPTION ( D )

@HarshPratapSingh