Writing Decimals as Rational Numbers

Q.

$\mathrm{1.666666......}$ is a rational number and can be expressed in $\frac{p}{q}$ form where $p$ and $q$ are integers. Then the value of $p+q$ is

1. The given number has a non-terminating and non-recurring decimal expansion and cannot be represented as $\frac{p}{q}$

2. $7$

3. $8$

4. $6$

Q. The decimal representation of a rational number is _______ in nature.

1. non terminating and non repeating
2. terminating
3. recurring
4. terminating or recurring

Q.

$2.35$ is: (a) an integer (b) a rational number (c) an irrational number (d) a natural number

1. an integer

2. a rational number

3. an irrational number

4. a natural number

Q.

A number, $x$ is represented in the simplest $\frac{p}{q}$ form. The decimal expansion of this number is $\mathrm{5.3333333333.....}$ Find the value of $p-q$

1. 13

2. 11

3. 12

4. 14

Q. $0.12\overline{45}$ is the decimal representation of the rational number .

1. $\frac{411}{300}$
2. $\frac{41}{3300}$
3. $\frac{411}{3300}$

Q. Express the rational number $\frac{14}{-21}$ in standard form

Q. Which of the following rational numbers is terminating?

1. $\frac{7}{3}$
2. $\frac{21}{80}$
3. $\frac{5}{6}$

Q. Let $\frac{p}{q}$ be a fraction expressed in the lowest form. If the numerator is increased by 2 and the denominator is increased by 1, the resulting fraction equals $\frac{1}{2}$. If, however, the numerator is increased by 1 and the denominator is decreased by 2, the resulting fraction equals $\frac{3}{5}$. The value of $(p+q)$ equals ($p,q$ are natural number )

1. $7$
2. $12$
3. $9$
4. $13$

Q. Which of the following are non-terminating decimals?

1. 1/2
2. 1/7
3. 2/3
4. 2/11
5. 2/40
6. 1/9
7. 1/13
8. 3/8
9. 9/13
10. 9/500

Q. $\frac{p}{q}$ form of the number $0.123\overline{456}$, where p and q are integers and $q\ne 0$, is ____

1. $\frac{3333}{99000}$
2. $\frac{41111}{999000}$
3. $\frac{12333}{99000}$
4. $\frac{41111}{333000}$

Q.

Solve: $625\times \frac{3}{5}$.

Q.

The rational number of the form $\frac{p}{q},q\ne 0$ , $p$ and $q$ are positive integers, which represents $0.1\overline{34}$ i.e., $\left(\mathrm{0.1343434......}\right)$ is

1. $\frac{134}{999}$
   
2. $\frac{133}{990}$
   
3. $\frac{134}{990}$
   
4. $\frac{133}{999}$

Q. How do you represent $0.3125$ in the form of $\frac{p}{q}$, where $p$ and $q$ are integers and $q$ is not zero?

1. $\frac{6}{20}$
2. $\frac{6}{18}$
3. $\frac{5}{25}$
4. $\frac{5}{16}$