Question

Write two irrational numbers between $0.21$ and $\mathrm{0.2222...}$

• A. $\mathrm{0.21010010001...}$
• B. $\mathrm{0.2102020202...}$
• C. $\mathrm{0.21020020002...}$
• D. $\mathrm{0.210101010101...}$

Answer 1

Answer: (A), (C)

The correct options are
A $\mathrm{0.21010010001...}$
C $\mathrm{0.21020020002...}$

$0.21$ and $\mathrm{0.2222...}$ are two rational numbers.

We know, between any two rational numbers, there are infinitely many irrational numbers.

An irrational number has non-terminating non-recurring decimal expansion.

Here, $\mathrm{0.21010010001...}$ and $\mathrm{0.21020020002...}$ are non-terminating non-recurring,

while $\mathrm{0.210101010101...}$ and $\mathrm{0.2102020202...}$ are non-terminating recurring.

Hence, the two irrational numbers are$\mathrm{0.21010010001...}$ and $\mathrm{0.21020020002...}$.

Thus, options $A$ and $C$ are the correct answers.