# NCERT Mathematics Class 9 Exemplar Ch 1 Number Systems Part 5

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**Exercise 1.3**

1. Find which of the variables x, y, z and u represent rational numbers and which irrational numbers:

(i)

(ii)

(iii)

(iv)

Answer: Rational numbers: (ii), (iii) Irrational numbers: (i), (iv)

2. Find three rational numbers between

(i) –1 and –2

(ii) and

(iii) and

(iv) and

Answer: (i) –1.1, –1.2, –1.3 (ii) 0.101, 0.102, 0.103 (iii), , (iv) , ,

3. Insert a rational number and an irrational number between the following :

(i) 2 and 3

(ii) 0 and 0.1

(iii) and

(iv) and

(v) 0.15 and 0.16

(vi) and

(vii) 2.357 and 3.121

(viii) .0001 and .001

(ix) 3.623623 and 0.484848

(x) 6.375289 and 6.375738

Answer: (i)

(ii)

(iii) ,

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

4. Represent the following numbers on the number line: 7, 7.2, ,

5. Locate , and on the number line.

6. Represent geometrically the following numbers on the number line:

(i)

(ii)

(iii)

(iv)

7. Express the following in the form , where p and q are integers and :

(i) 0.2

(ii)

(iii) 5.2

(iv)

(v)

(vi)

(vii) .

(viii) .

Answer: (i) , (ii) , (iii) , (iv) , (v) , (vi) , (vii) , (viii)

8. Show that 0.142857142857... =

9. Simplify the following:

(i) – + 4

(ii) +

(iii) ×

(iv) ÷ 3 ÷

(v) 3 + 2 +

(vi)

(vii) – + +

(viii) +

(ix) -

Answer: (i)

(ii)

(iii) 168

(iv)

(v)

(vi)

(vii) 0

(viii)

(ix)