Question

find one irrational number between the numbers a) and b) given a=0.1111....=01 ,b) 0.1101

Answer 1

Step-by-step explanation:

Given Find one irrational number between the numbers a) and b) given a=0.1111....=01 ,b) 0.1101

• Now consider the number p = 0.111101001000100001
• Now we have p as an irrational number since it is non terminating and non repeating decimal.  
• So now in the first two places of decimal b and p have similar digits and the third place has 0 whereas p has 1.
• Therefore b < p
• Also p and a have similar digits in first four places of decimal and in the fifth place p has 0 and a will have 1
• Therefore p < a
• Hence b < p < a
• So p is the irrational number between a and b

Reference link will be

https://brainly.in/question/4218937