Check If a Given Rational Number Is Terminating or Not

Q.

Question 1 (v)
Without actually performing the long division, state whether $\frac{29}{343}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Q.

Question 10
The decimal expansion of the rational number $\frac{14587}{1250}$ will terminate after

A) One decimal place
B) Two decimal places
C) Three decimal places
D) Four decimal places

Q.

S1 : $\frac{1323}{1400}$ is a non terminating decimal.
S2 : A number $\frac{p}{q}$ where p and q are co-primes is terminating if q is of the form $2^n{.3}^m$ where n and m are non-negative integers.

1. S1 is false and S2 is true

2. S1 is true and S2 is false

3. S1 and S2 are true.

4. S1 and S2 are false

Q. Decimal expansion of $\frac{7}{500}$ is _______.

1. Terminating
2. Non - terminating
3. Both recurring and terminating
4. Recurring

Q.

If x =$\frac{p}{q}$ , and q is not of the form $2^m{5}^n$ then x is terminating.

1. True

2. False

Q.

If a terminating decimal can be expressed in the form $\frac{p}{q}$ where p and q are co-prime integers and q ≠ 0, and q is of the form $2^m{5}^n$ .where m and n are non-negative integers.

1. True

2. False

Q. Check whether $\frac{3}{13}$ is
non-terminating, repeating decimals or terminating decimal number?

Q. Without doing any actual division, find which of the following rational number have terminating decimal representation:
$\frac{17}{40}$.

Q.

Question 6
Look at several examples of rational numbers in the form $\frac{p}{q}(q\ne 0)$ where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?