Unit 1: Real And Complex Numbers - Mathematics For Class IX (Science Group) - Solved Exercise 1.1

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Unit 1: Real And Complex Numbers
Exercise 1.1

1. Identify the following numbers as rational and irrational numbers and also write each one in separate column.
Additional Question
Vii) 0
Solution:
(For rational number: Nominator and denominator are integers and denominator is not equal to zero i.e. ^p/_q are integers & q ≠ 0.)
Ans: 0 is a rational number.

2. Convert the following into decimal fraction. Also indicate them as terminating and Non-terminating decimal fractions.

3. Represent the following rational numbers on number line.

OR

4. Can you make a list of all rational number between 1 and 2?
Ans: It is Infinite rational number because the the rational number between two whole numbers are always infinite.

And

(i) ⁵/₄ = 1.25
(ii) ³/₂ = 1.5
(iii) ⁷/₄ = 1.75
(iv) ⁹/₈ = 1.125

5. Give reason, why pi (π) is an irrational number?
Ans:  π = ²²/₇ = 3.14285....
Pi (π) is an irrational number because it has non-terminal and non recurring decimal fraction.

6. Tick (✓) the correct statements.
(i) ⁵/₇ is an example of irrational number. ✓
(ii) π is an irrational number. ✓
(iii) 0.31591... is an example of non-terminating and non-repeating decimal fraction. ✓
(iv) 0.123 is an example of recurring decimal fraction. x
(v) ¹/₃, ²/₃ are lying between 0 and 1. ✓
(vi) ¹ /_{√ 3} is an example of rational number. x

Examples