Question

a rational no. in its decimal expansion is 554.6023.what can you say about the prime factors of q,when this no. is expressed in the form p/q​

Answer 1

Since 554.6023 is a terminating decimal number so q must be of the form 2^m×5^n, where m, n are natural numbers.

554.6023= 5546023/10000

=5546023 / 2^4 x 5^4 = p/q

Here, q is of the form 2m × 5n, where m and n are natural numbers. The prime factors of p and q will be either 2 or 5 or both.