Question

# Find two irrational numbers lying between 0.1 and 0.12. Enter 1 if the numbers are 0.1010010001……. and 0.1101001000100001…..otherwise, enter 0.

Before proceeding with the question, we should know about irrational numbers. An irrational number is a real number that cannot be expressed as a ratio of integers. Again, the decimal expansion of an irrational number is neither terminating nor recurring. Real numbers which cannot be expressed in the form of $\dfrac{\text{p}}{\text{q}}$, where p and q are integers and $\text{q}\ne 0$ are known as irrational numbers. For example $\sqrt{2}$, $\sqrt{3}$ etc. Whereas any number which can be represented in the form of $\dfrac{\text{p}}{\text{q}}$, such that, p and q are integers and $\text{q}\ne 0$ is known as a rational number. For example $\dfrac{6}{13}$, $\dfrac{3}{7}$ etc.
Let $a=0.1$ and $b=0.12$. Here a and b are rational numbers.