Find a Rational and an Irrational Number Between Given Decimals
Question: Find a rational number and also an irrational number lying between \(0.3030030003…\) and \(0.3010010001…\).
Solution:
First arrange the numbers:
\[ 0.3010010001… < 0.3030030003... \]
Step 1: Rational Number
Choose a terminating decimal between them:
\[ 0.302 \]
This is a rational number.
Step 2: Irrational Number
Choose a non-terminating, non-repeating decimal between them:
\[ 0.302002000200002… \]
This number is irrational.
Final Answer:
- Rational number: \(0.302\)
- Irrational number: \(0.302002000200002…\)