Question

1. Without actual division, find which of the following rational numbers
are terminating decimals.
13/80​

Answer 1

Answer:

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 , the denominator is 80.

We have, 80 = 2 × 2 × 2 × 2 × 5.

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

Hence, must have a terminating decimal representation.

∴ Terminating decimal representation of = 0.1625

Answer 2

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