Question

Which one of the following is true about the prime factors of the denominator of the decimal expansion: 278.1782?

• A. It is a power of 5 only
• B. It is a power of 2 only
• C. It may have any factors
• D. It is a product of powers of 2 and 5

Answer 1

The correct option is D

It is a product of powers of 2 and 5

Recall the theorem : Let x be a rational number whose decimal expansion terminates.

Then x can be expressed in the form p /q where p and q are coprime, and the prime factorisation of q is of the form 2ⁿ5^m, where n, m are non-negative integers.

278.1782 is a terminating decimal expansion

factors of the denominator can be expressed as 2ⁿ 5^m

It is a product of powers of 2 and 5