Question

without actual division find which of the following rational number are terminating decimal 13/80

Answer 1

yes it is terminating decimal...as 80 has 2x2x2x2x5 as it's prime factors.

Answer 2

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 $\frac{13}{80}$ = 0.1625