Question

Is $(\pi -{\displaystyle \frac{22}{7}})$ a rational number, an irrational number or zero?

Answer 1

Hint: We are given difference of two number as: $(\pi -{\displaystyle \frac{22}{7}})$. Firstly, identify whether the numbers are rational or irrational. Then identify if the difference is rational or rational.

Complete step-by-step solution:
As we know that: $\pi$ is an irrational number. It also represents the ratio of the circumference to the diameter of a circle.
Also, ${\displaystyle \frac{22}{7}}$ is a rational number because it is represented in the form of ${\displaystyle \frac{p}{q}}$
Now, we need to find the difference of both numbers $(\pi -{\displaystyle \frac{22}{7}})$ is rational or irrational.
Since we know that the sum or difference of a rational and irrational number is always irrational. Therefore, the difference of $(\pi -{\displaystyle \frac{22}{7}})$ is also an irrational number.

Note: A rational number is a number that can be expressed as a fraction where both the numerator and the denominator in the fraction are integers. The denominator in a rational number cannot be zero. A rational number is expressed in the form of ${\displaystyle \frac{p}{q}}$, where $q\ne 0$. Their decimal expansion is finite or repeating decimals. Do not consider $\pi$ as ${\displaystyle \frac{22}{7}}$ and then write the result as 0, it will not be correct in this question. Irrational numbers are real numbers that can’t be written as a simple fraction. Their decimal expansion is non-finite or non-repeating decimals.