AP State Syllabus AP Board 9th Class Maths Solutions Chapter 1 Real Numbers Ex 1.1 Textbook Questions and Answers.

## AP State Syllabus 9th Class Maths Solutions 1st Lesson Real Numbers Exercise 1.1

Question 1.

a) Write any three rational numbers.

Solution:

\(\frac{3}{4}, \frac{5}{9}, \frac{2}{7}\)

b) Explain rational number is in your own words.

Solution:

A number which can be expressed in algebraic form i.e., in \(\frac { p }{ q }\) form is called a rational number.

E.g.: \(\frac { 3 }{ 5 }\), \(\frac { -4 }{ 9 }\) etc.

Question 2.

Give one example each to the following statements.

i) A number which is rational but not an integer.

Solution:

7/11

ii) A whole number which is not a natural number.

Solution:

‘0’ (Zero)

iii) An integer which is not a whole number.

Solution:

-8

iv) A number which is natural number, whole number, integer and rational number.

Solution:

5

v) A number which is an integer but not a natural number.

Solution:

-4

Question 3.

Find five rational numbers between 1 and 2.

Solution:

Question 4.

Five rational numbers between \(\frac { 2 }{ 3 }\) and \(\frac { 3 }{ 5 }\)

Solution:

Question 5.

Represent \(\frac { 8 }{ 5 }\) and \(\frac { -8 }{ 5 }\) on a number line.

Solution:

Step – 1 : Draw a number line.

Step – 2 : Divide each unit into 5 equal parts.

Step – 3 : Take 8 – equal parts from ‘0’ on its right side and mark it as \(\frac { 8 }{ 5 }\) (similarly) on left side \(\frac { -8 }{ 5 }\) .

Question 6.

Express the following rational numbers as decimal numbers.

Solution:

I. i) \(\frac { 242 }{ 1000 }\) .

ii) \(\frac { 354 }{ 500 }\) .

iii) \(\frac { 2 }{ 5 }\) .

iv) \(\frac{115}{4}\)

Solution:

i) \(\frac { 242 }{ 1000 }\) = 0.242

ii) \(\frac{354}{500}\)

\(=\frac{354 \times 2}{500 \times 2}\)

\(=\frac{708}{1000}\)

\(=0.708\)

iii) \(\frac{2}{5}\)

\(=\frac{2 \times 2}{5 \times 2}\)

\(=\frac{4}{10}\)

\(=0.4\)

iv)

II. i) \(\frac{2}{3}\)

Solution:

ii) \(\frac{-25}{36}\)

Solution:

iii) \(\frac{22}{7}\)

Solution:

iv) \(\frac{11}{9}\)

Solution:

Question 7.

Express each of the following decimals in \(\frac{p}{q}\) form where q ≠ 0 and p, q are integers.

i) 0.36

Solution:

0.36 = \(\frac{36}{100}=\frac{9}{25}\)

ii) 15.4

Solution:

15.4 = \(\frac{154}{10}=\frac{77}{5}\)

iii) 10.25

Solution:

10.25 = \(\frac{1025}{100}=\frac{41}{4}\)

iv) 3.25

Solution:

3.25 = \(\frac{325}{100}=\frac{13}{4}\)

Question 8.

Express each of the following decimal number in the \(\frac { p }{ q }\) form.

i) \(0 . \overline{5}\)

Solution:

Let x = \(0 . \overline{5}\) = 0.5555

Multiplying both sides by 10

ii) \(3 . \overline{8}\)

Solution:

Let x = \(3 . \overline{8}\)

(i.e) x = 3.888 ………..

Multiplying both sides by 10

iii) \(0 . \overline{36}\)

Solution:

Let x \(0 . \overline{36}\)

(i.e) x = 0.363636 ………..

Multiplying by 100 on both sides

iv) \(3.12 \overline{7}\)

Solution:

Let x = \(3.12 \overline{7}\)

x = 0.12777

Multiplying by 10 on both sides

Question 9.

Without actually dividing find which of the following are terminating

decimals.

i) \(\frac { 3 }{ 25 }\)

Solution:

Check the denominator, if it consists of 2’s or 5’s or combination of both then only it reduces to a terminating decimal.

25 = 5 x 5

Hence \(\frac { 3 }{ 25 }\) is a terminating decimal.

ii) \(\frac { 11 }{ 18 }\)

Solution:

Denominator 18 = 2 × 3 × 3,

hence \(\frac { 11 }{ 18 }\) is a non-terminating decimal 13

iii) \(\frac { 13 }{ 20 }\)

Denominator 20 = 2 × 2 × 5,

hence \(\frac { 13 }{ 20 }\) is a terminating decimal.

iv) \(\frac { 41 }{ 42 }\)

Solution:

Denominator 42 = 2 × 3 × 7,

hence \(\frac { 41 }{ 42 }\) is a non-terminating decimal.