Question

Which of the following rational numbers has terminating decimal representation?  23/72 61/75 17/50 11/14​

Answer 1

Answer:

Solution :

We know that if the denominator of a rational number has no prime factors other than 2 or 5, then it is expressible as a terminating, otherwise it has non - terminating repeating decimal representation. Thus, we will have to check the prime factors of the denominators of each of the given rational numbers.

In \frac{13}{80}

80

13

, the denominator is 80.

We have, 80 = 2 × 2 × 2 × 2 × 5.

Thus, 80 has only 2 and 5 as prime factors.

Hence, \frac{13}{80}

80

13

must have a terminating decimal representation.

∴ Terminating decimal representation of \frac{13}{80}

80

13

= 0.1625