Question

Let a =0.1001000100001 . and b= 0.101001000100001.
a) Write two irrational numbers between a and b.
b) Show that a and b are irrational numbers such that a <b.
c) Write two rational numbers between a and b.​

Answer 1

A - 0.1111111111111111.

B - 0.1222234557.

Answer 2

Answer:

a) 2 irrational nos. between a and b are 0.1002000200002..... and 0.10071000700007.....

b) In thousandths place in a, the digit is 0, whereas, in the thousandths place in b, the digit is 1. 1 is greater than 0, hence, a<b.

c) 2 rational nos. between a and b are 0.1002 and 0.1007.

(In (a) and (c) parts, any irrational and rational no. respectively lying between 0.1001000100001 between 0.101001000100001 can be taken. It is not necessary to write the nos. I have written)