Find Two Rational Numbers Between Given Decimals
Question: Give two rational numbers lying between \(0.232332333233332…\) and \(0.212112111211112…\).
Concept Used:
Between any two real numbers, there are infinitely many rational numbers. :contentReference[oaicite:0]{index=0}
Solution:
First, compare the given numbers:
\[ 0.212112111211112… < 0.232332333233332... \]
Now choose simple terminating decimals between them.
We can clearly see:
\[ 0.22 \text{ lies between them} \]
Also,
\[ 0.23 \text{ lies between them} \]
Verification:
\[ 0.212112111211112… < 0.22 < 0.23 < 0.232332333233332... \]
Final Answer:
Two rational numbers are:
- \(0.22\)
- \(0.23\)
Conclusion:
Any terminating decimal is a rational number, and we can always find infinitely many such numbers between two given numbers.