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

Solution:

327.7081 is the terminating decimal number.

It represents a rational number and also its denominator must have the form 2^m x 5ⁿ.

327.7081 = 3277081/10000 = p/q

q = 10⁴ = 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5 = 2⁴ × 5⁴ = (2 × 5)⁴

The prime factors of q are 2 and 5

Therefore, the prime factors of q are 2 and 5.

✦ Try This: A rational number in its decimal expansion is 43.123456789. What can you say about the prime factors of q, when this number is expressed in the form p/q ? Give reasons

43.123456789 is the terminating decimal number.

It represents a rational number and also its denominator must have the form 2m × 5n.

43.123456789 = 43123456789/1000000000 = p/q

= 43123456789/ 2⁹ x 5⁹

Now it's in the form of p/q.

The prime factors of q are 2 and 5

Therefore, the prime factors of q are 2 and 5

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 1

NCERT Exemplar Class 10 Maths Exercise 1.2 Problem 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

Summary:

A rational number in its decimal expansion is 327.7081. The prime factors of q, when this number is expressed in the form p/q are 2 and 5

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