Question

Write three irrational numbers between \[0.202002000200002......\] and \[0.203003000300003........\]
This question has multiple correct options
A. \[0.20201001000100001.........\]
B. \[0.202020020002........\]
C. \[0.202030030003.......\]
D. \[0.203030030003......\]

Answer 1

Hint: Here there are infinite irrational numbers between the given irrational numbers. So, we will go for optional verification. The irrational numbers greater than \[0.202002000200002......\] and less than \[0.203003000300003........\] are correct options.

Complete step-by-step answer:
Given irrational numbers are \[0.202002000200002......\] and \[0.203003000300003........\]
We know that between any two irrational numbers there exists infinite irrational numbers.
So, we will go for option verification.
A. \[0.20201001000100001.........\]
Clearly \[0.20201001000100001.........\] is greater than \[0.202002000200002......\] and less than \[0.203003000300003........\]
Thus, option A. \[0.20201001000100001.........\] is correct.
B. \[0.202020020002........\]
Clearly \[0.202020020002........\] is greater than \[0.202002000200002......\] and less than \[0.203003000300003........\]
Thus, option B. \[0.202020020002........\] is correct.
C. \[0.202030030003.......\]
Clearly \[0.202030030003.......\] is greater than \[0.202002000200002......\] and less than \[0.203003000300003........\]
Thus, option C. \[0.202030030003.......\] is correct.
D. \[0.203030030003......\]
Here, \[0.203030030003......\] is greater than \[0.202002000200002......\] and \[0.203003000300003........\]
Thus, option D. \[0.203030030003......\] is incorrect.

Note: Irrational numbers are numbers that cannot be expressed as the ratio of two whole numbers. This is opposed to rational numbers. Irrational numbers have decimal expansions that neither terminate nor become periodic.