Question

The decimal expansion of $\pi $ is:
A. A whole number
B. Terminating
C. Non – terminating but repeating
D. Non – terminating but non – repeating

Answer 1

Hint: First of all we will have to know about $\pi $. Actually, it is the ratio of the circumference of any circle to the diameter of that circle. The value of $\pi $ is equal to $\dfrac{22}{7}$ in rational form but in decimal we cannot calculate its exact values. In decimal it is equal to 3.141592……

Complete step-by-step answer:
We have been asked to find the decimal expansion of $\pi $.
Since, we know that $\pi $ is the ratio of the circumference of any circle to the diameter of that circle and the value of $\pi $ in rational form is equal to $\dfrac{22}{7}$. But, on decimal form we cannot find its exact value and it is equal to 3.141592…….
So, we will check all the options one by one.
A. Whole number
$\pi =3.141592......$ but as we know whole number are counting number including zero.
Hence, this option is incorrect.
B. Terminating
We know that terminating means a decimal having finite number after the decimal point but we can’t find the value of $\pi $ upto finite value.
Hence, this option is incorrect.
C. Non – terminating but repeating
It is true that the decimal expansion of $\pi $ is non – terminating but its digits not repeating after the decimal.
Hence, this option is incorrect.
D. Non – terminating but non – repeating
It is true that the decimal expansion of $\pi $ is non – terminating as well as non – repeating.
Hence, this option is correct.
Therefore, the correct option is D.

Note: Also, remember that fact about $\pi $ that the ratio of circumference of any circle to the diameter of that circle doesn’t change regardless of the circle’s size, this ratio always equal to $\pi $.
Also, while solving the questions we usually take \[\pi =\dfrac{22}{7}\] or in decimal form it is 3.14.