Question

Without actual division find weather the decimal expansion of rational no 39/240 is terminating or reccuring​

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