Question

Without actual division, find which of the following fractions are

terminating decimal : (i) 19/55
(ii)37/78​

Answer 1

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}

, 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}

must have a terminating decimal representation.

∴ Terminating decimal representation of

= 13/80 = 0.1625