Find Two Rational Numbers Between Given Decimals
Question: Give two rational numbers lying between \(0.515115111511115…\) and \(0.5353353335…\).
Concept Used:
Between any two real numbers, there are infinitely many rational numbers, so we can always choose convenient terminating decimals between them. :contentReference[oaicite:0]{index=0}
Solution:
First compare the numbers:
\[ 0.515115111511115… < 0.5353353335... \]
Now choose simple terminating decimals between them.
Clearly,
\[ 0.52 \text{ lies between them} \]
Also,
\[ 0.53 \text{ lies between them} \]
Verification:
\[ 0.515115111511115… < 0.52 < 0.53 < 0.5353353335... \]
Final Answer:
- \(0.52\)
- \(0.53\)
Conclusion:
Any terminating decimal is a rational number, and infinitely many such numbers can be found between two given numbers.