Q7 of 51 Page 1

Give two rational numbers lying between 0.232332333233332…. and 0.212112111211112.

Let a = 0.212112111211112

And, b = 0.232332333233332….


Clearly a < b because in the second decimal place a has digit 1 and b has digit 3


If we consider rational numbers in which decimal place has the digit 2, then they will lie between a and b


Let,


x = 0.22


y = 0.22112211…


Then,


a < x < y < b


Hence, x and y are required rational numbers.


More from this chapter

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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.

 8

Give two rational numbers lying between 0.515115111511115…. and 0.5353353335….

 9

Find one irrational number between 0.2101 and 0.2222 ….= .