Question

Find a rational number and also an irrational number lying between the numbers 0.3030030003.... and 0.3010010001...?

Answer 1

Hint: For solving this problem, we must know the basic difference between rational and irrational numbers. Rational numbers are terminating while irrational numbers are non-terminating and non-recurring. By using this fact, we obtained the desired numbers.

Complete step-by-step answer:
Rational numbers are those numbers which can be represented in the form of $\dfrac{p}{q}$, where p is the numerator and q is the denominator. P and Q may belong to any of the three categories such as natural, whole or integers.
And, an irrational number is any real number other than a rational number.
As given in our problem, we have to find a rational and an irrational number between the numbers 0.3030030003.... and 0.3010010001...
So, for a rational number:
$0.3030030003.....<0.302<0.3010010001....$
This implies that 0.302 is a rational number between 0.3030030003.... and 0.3010010001...
Now, for an irrational number:
$0.3030030003.....<0.3020020002......<0.3010010001....$
This implies that 0.3020020002…. is a irrational number between 0.3030030003.... and 0.3010010001...
Note: The key step for solving this problem is the knowledge of the number system and particularly rational and irrational numbers. The basic idea of a rational and irrational number system is good enough to solve both the parts. This knowledge is helpful in solving complex problems.