Check if a Given Rational Number is Terminating or Not

Q.

Without actual division find which of the following rationals are terminating decimal:

1. $\frac{13}{80}$

2. $\frac{7}{28}$

3. $\frac{5}{12}$

4. $\frac{8}{35}$

5. $\frac{16}{125}$

Q. Which of the following rational numbers is a non-terminating and repeating decimal?

1. $\frac{3}{250}$
2. $\frac{7}{25}$
3. $\frac{17}{32}$
4. $\frac{17}{36}$

Q. Assertion (A): $\frac{29}{9261}$ will have a non-terminating, non-repeating decimal expansion.
Reason (R): Let $a=\frac{p}{q}$ be a rational number such that $p$ and $q$ are co-prime and the prime factorisation of $q$ is of the form $2^n\times 5^m$, where $n$ and $m$ are non-negative integers. Then $a$ has a decimal expansion, which is non-terminating.

1. (A) is true and (R) is false
2. (A) is false and (R) is the correct explanation of (A)
3. (A) and (R) are true and (R) is the correct explanation of (A)
4. Both (A) and (R) are false