Question

If $x = \dfrac{p}{q}$ be rational number such that the prime factorization of $q$ is not of the form ${2^n}{5^m}$, where $n,m$ are non-negative integers. Then $x$ has a decimal expansion which is terminating.
A. True
B. False
C. Neither
D. Either

Answer 1

Hint: Here, we will see that $x$is a rational number or irrational number. Then, we will check if $q$ is in positive form or not. Then we will get the desired result.


Complete step by step solution:
Here $x = \dfrac{p}{q},$ where $p$ and $q$ are integers.
Here \[q\] is not in the form of ${2^n} \times {5^m}$ where \[n,m\] are non-negative integers.
Hence the correct option is B.

Additional information: If $q = {2^n} \times {5^m}$, where $n\,and\,\,m$ are integers.
Then $P$ is divided by $2\,\,and\,\,2$ or P is divided by $10$
If the integer is divided by $10$ we will get a terminated decimal fraction.

Note: Students should carefully follow the instructions given in the question, if $q$ is not of form \[{2^n} \times {5^m}\] then definitely $q$ can take any of the values $3,6,9,13,15$….etc.