Expressing Decimals as Rational Numbers

Q.

Find three different irrational numbers between $\frac{5}{7}$ and $\frac{9}{11}$.

Q.

Find three different irrational numbers between $\frac{2}{3}$ and $\frac{3}{4}$.

Q.

The number $1.\overline{27}$ in the form $\frac{p}{q}$, where p and q are integers and q $\ne$ 0, is

1. $\frac{14}{9}$

2. $\frac{14}{11}$

3. $\frac{14}{13}$

4. $\frac{14}{15}$

Q.

Express each of the following decimals in the form $\frac{p}{q}$ :

$\left(i\right)0.39$

$\left(ii\right)0.750$

$\left(iii\right)2.15$

$\left(iv\right)7.010$

$\left(v\right)9.90$

$\left(vi\right)1.0001$

Q.

Express each of the following decimals in the form $\frac{p}{q}$ :

(i) 0.$\overline{4}$ (ii) $0.\overline{37}$

(iii) $0.\overline{54}$ (iv) $0.\overline{621}$

(v) $125.\overline{3}$ (vi) $4.\overline{7}$

(vii) $0.4\overline{7}$

Q.

$0.66666$in the form of $\frac{p}{q}$ is :

Q.

Question 3
Find five rational numbers between $\frac{3}{5}and\frac{4}{5}$.

Q.

Express 2.5434343..... In the form of p/q where p and q are integers and q is not equal to zero.

Q.

Prime factors of the denominator of a rational number with the decimal expansion $44.123$ are

1. $2,3$

2. $2,3,5$

3. $2,5$

4. $3,5$

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

Q.

Find three different irrational numbers between $\frac{3}{5}$ and $\frac{7}{8}$.

Q.

Four rational numbers between $3$ and $4$ are:

1. $\frac{3}{5},\frac{4}{5},1,\frac{6}{5}$
2. $\frac{13}{5},\frac{14}{5},\frac{16}{5},\frac{17}{5}$
3. $3.1,3.2,4.1,4.2$
4. $3.1,3.2,3.8,3.9$

Q.

The simplest form of 0.12$\overline{3}$ is

(a)$\frac{41}{330}$ (b)$\frac{37}{330}$ (c)$\frac{41}{333}$ (d) none of these

Q.

The simplest form of $1.\overline{6}$ is

(a)$\frac{833}{500}$

(b)$\frac{8}{5}$

(c)$\frac{5}{3}$

(d) none of these

Q.

The value of 2.$\overline{45}$ + 0.$\overline{36}$ is

(a)$\frac{67}{33}$

(b)$\frac{24}{11}$

(c)$\frac{31}{11}$

(d)$\frac{167}{110}$

Q.

The sum of 0.$\overline{3}$ and $0.\overline{4}$ is

(a)$\frac{7}{10}$

(b)$\frac{7}{9}$

(c)$\frac{7}{11}$

(d)$\frac{7}{99}$

Q.

The value of $0.\overline{2}$ in the form $\frac{p}{q}$, where p and q are integers and $q\ne 0$, is

(a) $\frac{1}{5}$

(b) $\frac{2}{9}$

(c) $\frac{2}{5}$

(d) $\frac{1}{8}$

Q.

Find three different irrational numbers between $-\frac{3}{7}$ and $-\frac{2}{7}$.

Q.

Express the following in the form $\frac{p}{q}$, where $p$ and $q$ are integers and q ≠ 0.
$0.\overline{001}$

Q. 1.666666...... is a rational number and can be expressed in $\frac{p}{q}$ form.
Then $p+q$ is .

1. 8
2. 9
3. 6

Q.

How do you write $0.4$ as a fraction?

Q.

What is the approximate value of $\frac{1}{e}$?

Q. Question 9
The value of 1.999 ….. in the form of $\frac{p}{q}$, where p and q are integers and $q\ne 0$, is

A) $\frac{19}{10}$
B) $\frac{1999}{1000}$
C) $2$
D) $\frac{1}{1}$

Q. Express $0.2\overline{37}$ in the form of $\frac{p}{q}$

Q.

Represent -25.6875 in rational form.

1. -411/16

2. 25/68575

3. 256/8750

4. 2568/7500

Q. $0.8+0.\overline{7}+0.4\overline{3}=$ .

1. $\frac{182}{90}$
2. $\frac{181}{90}$
3. $\frac{90}{18}$
4. $\frac{180}{90}$

Q.

The simplest form of $0.3\overline{2}$ is

(a)$\frac{16}{45}$

(b)$\frac{32}{99}$

(c)$\frac{29}{90}$

(d) none of these

Q.

Represent 15.712121212…in a rational form. [4 MARKS]

Q. Express the following in the form $\frac{p}{q}$, wher $p$ and $q$ are integers and $q\ne 0.$
(i) $0.\overline{6}$
(ii) $0.4\overline{7}$
(iii) $0.\overline{001}$

Q. Express the following in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q\ne 0$
$0.\overline{001}$