Q4 of 51 Page 1

Identify the following as rational or irrational numbers. Give the decimal representation of rational numbers:

(i) (ii) 3 (iii) (iv) (v) (vi)

(i) = 2 =

can be written in the form of , so it is a rational number.


Its decimal expansion is 2.0


(ii) 3 = 3


= 3 * 3


= 9


Since, the product of a rational and an irrational is an irrational number.


Therefore, 9 is an irrational;


3 is an irrational number


(iii) We have,


=


= 1.2


Every terminating decimal is a rational number, so 1.2 is a rational number.


(iv) we have,


= =


=


Quotient of a rational and an irrational number is irrational number. Therefore, it is an irrational number.


(v) - = -


= - 8 = -8/1


AS it can be expressed in the form of , so it is a rational number.


(vi) = 10 =


Thus it can be expressed in the form of , so it is a rational number.


More from this chapter

All 51 →
2

Explain, how irrational numbers differ from rational numbers?

 3

Examine, whether the following numbers are rational or irrational:

(i) (ii) (iii) 2+ (iv)


(v) (vi) (-2)2 (vii) (2-) (2+) (viii)


(ix) -2 (x) (xi) (xii) 0.3796 (xiii) 7.478478


(xiv) 1.101001000100001…..

 5

In the following equations, find which variables x, y, z etc. represent rational or irrational numbers:

(i) x2 = 5 (ii) y2 = 9 (iii) z2 = 0.04 (iv) u2 = (v) v2 = 3 (vi) w2 = 27 (vii) t2 = 0.4

 6

Give an example of each, of two irrational numbers whose:

(i) Difference is a rational number.


(ii) Difference is an irrational number.


(iii) Sum is a rational number.


(iv) Sum is an irrational number.


(v) Product is a rational number.


(vi) Product is an irrational number.


(vii) Quotient is a rational number.


(viii) Quotient is an irrational number.