Question

For which of the following value (s) of p,251/(2cube × p square) is non-terminating recurring decimal?441/(2square × 5 seven × 7square) is a dash decimal​

Answer 1

Given: $\[\frac{{251}}{{\left( {{2^3} \times {p^2}} \right)}}\]$.

To find: the value of p.

Solution:

Check prime factors of denominators of given fraction .

• if Prime factor are in the form of $2^m$ or $5^n$ or $2^m \times 5^n$ . Than the given fraction is a terminating decimal expansion .
• if prime factors are other than $2^m$ or $5^n$ or $2^m \times 5^n$  , than the given fraction is a non - terminating decimal expansion ..

Note that from the question

$\[\frac{{251}}{{\left( {{2^3} \times {p^2}} \right)}}\]=$ Is a terminating decimal expansion .

Understand that,

It is only possible when value of p is equal to 5 . Because then denominator will be in the form of $2^m \times 5^n$ .

Hence, the value of p is 5.