SChand CLASS 9 Chapter 1 Rational number and Irrational number Exercise 1(A)

 Exercise 1(A)

---

Q1 | Ex-1A |Class 8 |Rational Numbers  and Irrational Number  | S.Chand | New Learning | Composite mathematics | myhelper

OPEN IN YOUTUBE

Question 1

(i) Find a rational numbers between $\frac{1}{2}\text{ and } \frac{3}{4}$

Sol :

$=\frac{1}{2}\left[\frac{1}{2} + \frac{3}{4}\right]$

$=\frac{1}{2}\left[\frac{2+3}{4}\right]$

$=\frac{1}{2} \times \frac{5}{4}$

$=\frac{5}{8}$

(ii) Find two rational numbers between 0.1 and 0.2

Sol :

First$=\frac{1}{2}[0.1+0.2]$

$=\frac{1}{2} \times 0 \cdot 3$

=0.15

$=\frac{3}{20}$

Second$=\frac{1}{2}\left[\frac{3}{20}+\frac{2}{10}\right]$

$=\frac{1}{2}\left[\frac{3+4}{20}\right]$

$=\frac{1}{2} \times \frac{7}{20}$

$=\frac{7}{40}$

Numbers are $\frac{3}{20} \text{ and } \frac{7}{40}$

(iii) How many rational numbers can you find between two given rational numbers?

Sol :

There are infinite numbers of rational numbers between two rational numbers 

---

Q2 | Ex-1A |Class 8 |Rational Numbers  and Irrational Number  | S.Chand | New Learning | Composite mathematics | myhelper

OPEN IN YOUTUBE

Question 2

Find two rational numbers between 

(i) $\frac{4}{5}$ and $\frac{7}{13}$

Sol :

First$=\frac{1}{2}\left[\frac{4}{5}+\frac{7}{13}\right]$

$=\frac{1}{2}\left[\frac{52+35}{65}\right]$

$=\frac{87}{130}$

Second

$=\frac{1}{2}\left[\frac{87}{130}+\frac{7}{13}\right]$

$=\frac{1}{2}\left[\frac{87+10}{130}\right]$

$=\frac{1}{2}\left[\frac{157}{130}\right]$

$=\frac{157}{260}$

(ii) $\frac{3}{4}$ and $1 \frac{1}{5}$

Sol :

First$=\frac{1}{2}\left[\frac{3}{4}+\frac{6}{5}\right]$

$=\frac{1}{2}\left[\frac{15+24}{20}\right]$

$=\frac{1}{2}\left[\frac{39}{20}\right]$

$=\frac{39}{40}$

Second$\Rightarrow \frac{1}{2}\left[\frac{39}{40}+\frac{6}{5}\right]$

$\Rightarrow \frac{1}{2}\left[\frac{39+118}{40}\right]$

$=\frac{1}{2} \times \frac{87}{40}$

$=\frac{87}{80}$

---

Q3 | Ex-1A |Class 8 |Rational Numbers  and Irrational Number  | S.Chand | New Learning | Composite mathematics | myhelper

OPEN IN YOUTUBE

Question 3

Find three rational numbers between 0 and 0.2

Sol :

(i) Rational number between 0 and 0.2

First$=\frac{1}{2}[0+0.2]$

=0.1

Second

$=\frac{1}{2}[0+0.1]$

$=\frac{1}{2}[0.1]$

=0.05

Third

$=\frac{1}{2}[0.1+0.2]$

$=\frac{1}{2}[0.3]$

=0.15

∴Three rational numbers are 0.05 , 0.1 and 0.15

---

Q4 | Ex-1A |Class 8 |Rational Numbers  and Irrational Number  | S.Chand | New Learning | Composite mathematics | myhelper

OPEN IN YOUTUBE

Question 4

Find three rational numbers between 3 and 4.

Sol :

Rational number between 3 and 4

$=\frac{1}{9}[3+4]$

$=\frac{1}{2} \times 7$

$=\frac{7}{2}$

Rational number between 3 and $\frac{7}{2}$

$=\frac{1}{2}\left[3+\frac{7}{2}\right]$

$=\frac{1}{2} \times \frac{6+7}{2}$

$=\frac{13}{4}$

Rational number between $\frac{7}{2}$ and 4

$=\frac{1}{2}\left[\frac{2}{2}+4\right]$

$=\frac{1}{2}\left[\frac{7+8}{2}\right]$

$=\frac{1}{2} \times \frac{15}{2}$

$=\frac{15}{4}$

∴Three numbers are 

$\frac{13}{4}, \frac{7}{2}$ and $\frac{15}{4}$

---

Q5 | Ex-1A |Class 8 |Rational Numbers  and Irrational Number  | S.Chand | New Learning | Composite mathematics | myhelper

OPEN IN YOUTUBE

Question 5

Find the rational number that is one seventh of the way from $1\frac{3}{4}$ to $4\frac{3}{8}$

Sol :

$=1 \frac{3}{4}$ to $4 \frac{3}{8}$

$=\frac{7}{4}$ to $\frac{35}{8}$

$=\frac{14}{8}$ to $\frac{35}{8}$

There are 21 terms between 14 and 35

i.e. $\frac{15}{8}, \frac{16}{8}, \frac{17}{8}, \frac{18}{8}\dots \frac{38}{8}$

$\Rightarrow \frac{1}{7}$ th of 21 terms

$=21 \times \frac{1}{7}$

=3rd

3rd term

$=\frac{17}{8} \text{ or } 2\frac{1}{8}$

---

Q6 | Ex-1A |Class 8 |Rational Numbers  and Irrational Number  | S.Chand | New Learning | Composite mathematics | myhelper

OPEN IN YOUTUBE

Question 6

Find four rational numbers between -1 and $-\frac{1}{2}$

Sol :

Rational number between $-1 \text{ and } \frac{1}{-2}$

$\left.=\frac{1}{2}\left[-1+\frac{1}{-2}\right)\right]$

$=\frac{1}{2}\left[ \frac{2+1}{-2} \right]$

$=\frac{1}{2}\left(-\frac{3}{2}\right)$

$=\frac{-3}{4}$

Rational number between -1 and $\left[\frac{-3}{4}\right]$

$=\frac{1}{2}\left[-1+\frac{(-3)}{4}\right]$

$=\frac{1}{2}\left[-1\frac{-3}{4}\right]$

$=\frac{1}{2}\left(\frac{-7}{4}\right)$

$=\frac{-7}{8}$

Rational number between $\frac{-3}{4}$ and $\frac{-1}{2}$

$=\frac{1}{2}\left[\frac{-3}{4}+\left(\frac{-1}{2}\right)\right]$

$=\frac{1}{2}\left[\frac{-3}{4}-\frac{1}{2}\right]$

$=\frac{1}{2}\left[\frac{-5}{4}\right]$

$=\frac{-5}{8}$

Rational number between $\frac{-5}{8}$ and $\frac{-1}{2}$

$=\frac{1}{2}\left[\frac{-5}{8}+\left(\frac{-1}{2}\right)\right]$

$=\frac{1}{2}\left[-\frac{5}{8}-\frac{1}{2}\right]$

$=\frac{1}{2}\left[\frac{-5-4}{8}\right]$

$=\frac{1}{2}\left[-\frac{9}{8}\right]$

$=\frac{-9}{16}$

Four numbers are

$\frac{-3}{4}, \frac{-7}{8}, \frac{-5}{8}, \frac{-9}{16}$

---

Q7 | Ex-1A |Class 8 |Rational Numbers  and Irrational Number  | S.Chand | New Learning | Composite mathematics | myhelper

OPEN IN YOUTUBE

Question 7

Express $\frac{12}{125}$ as decimal fraction.

Sol :

$\frac{12}{125}$

Divide 12 by 125

---

Q8 | Ex-1A |Class 8 |Rational Numbers  and Irrational Number  | S.Chand | New Learning | Composite mathematics | myhelper

OPEN IN YOUTUBE

Question 8

Find a vulgar fraction equivalent to 0.03.

Sol :

$0.0\overline{3}$

=0.033333

Let x=0.033333...

10x=0.33333...

100x=3.3333...

Subtract (1) and (2)

90x=3.00...

$\begin{aligned} x &=\frac{3}{90} \\ &=\frac{1}{30} \end{aligned}$

---

Q9 | Ex-1A |Class 8 |Rational Numbers  and Irrational Number  | S.Chand | New Learning | Composite mathematics | myhelper

OPEN IN YOUTUBE

Question 9

Express the following rational numbers in the form $\frac{p}{q},$p , q are integers , q≠0

(i) $6 . \overline{46}$=6.464646..

Sol :

Let x=6.4646464..(i)

100x=646.4646...(ii)

Subtract (i) from (ii)

99x=646-6

99x=640

$x=\frac{640}{99}$

(ii) $0 . 1\overline{36}$=0.136136363

Sol :

Let x=0.13636363...

10x=1.363636..(i)

100x=136.363636...(ii)

Subtracting (i) from (ii)

90x=135

$\begin{aligned} x &=\frac{135}{90} \\ &=\frac{27}{18} \end{aligned}$

(iii) $3.\overline{146}$

Sol :

Let x=$3.\overline{146}$

x=3.146146146...(i)

1000x=3146.146146.....(ii)

Subtracting (i) from (ii)

999x=3143

$x=\frac{3143}{999}$

(iv) $-5.\overline{12}$

Sol :

Let x=$-5.\overline{12}$

x=-5.121212....(i)

100x=-512.121212...(ii)

Subtracting (i) from (ii)

99x=-507

$x=\frac{-507}{99}=\frac{-169}{33}$

---

Q10 | Ex-1A |Class 8 |Rational Numbers  and Irrational Number  | S.Chand | New Learning | Composite mathematics | myhelper

OPEN IN YOUTUBE

Question 10

Write the terminating decimal numeral for the given rational numbers.

(i) $=\frac{7}{4}$

Sol :

(ii) $\frac{29}{50}$

Sol :

(iii) $\frac{17}{32}$

Sol :

---

Q11 | Ex-1A |Class 8 |Rational Numbers  and Irrational Number  | S.Chand | New Learning | Composite mathematics | myhelper

OPEN IN YOUTUBE

Question 11

Write the repeating decimal for each of the following and use a bar to shoe the repetend.

(i) $\frac{1}{9}$
Sol :

$0.1111....=0.\overline{1}$

(ii) $\frac{-4}{3}$
Sol :

$-1.3333....=-1.\overline{3}$

(iii) $\frac{1}{6}$

Sol :

$0.1666....=0.1\overline{6}$