Question

decimal expansion of P by Q is non terminating and non repeating if for any two whole numbers M and n​

Answer 1

(i) 58 = 523×50. So, 58 is a terminating decimal.

(ii) 91280 = 928×51. So, 91280 is a terminating decimal.

(iii) 445 = 432×51. Since it is not in the form \(\frac{p}{2^{n} × 5^{m}}\), So, 445 is a non-terminating, recurring decimal.

For example let us take the cases of conversion of rational numbers to terminating decimal fractions:

(i) 12 is a rational fraction of form pq. When this rational fraction is converted to decimal it becomes 0.5, which is a terminating decimal fraction.

(ii) 125 is a rational fraction of form pq. When this rational fraction is converted to decimal fraction it becomes 0.04, which is also an example of terminating decimal fraction.

(iii) 2125 is a rational fraction form pq. When this rational fraction is converted to decimal fraction it becomes 0.016, which is an example of terminating decimal fraction.

Answer 2

Q can be expressed in the form of 2m * 5n