What is the Value of Pi?
When the value of the diameter of a circle is divided by the corresponding circumference of the same circle, we get the value of pi. The diameter of a circle is defined as the longest line segment passing through the centre of the circle. We get \(\frac{22}{7}\) = 3.142857… when we divide the circumference by the diameter, which is the value of pi. It’s important to note that no matter how large a circle we draw, the circumference to diameter ratio will always be the same. In mathematics, the symbol for pi is \(\pi\). It is referred to as a mathematical constant because its value remains constant.
Learn More About the Value of Pi through This Video
Value of Pi(\(\pi\)) as a Fraction
The fractional value of pi is \(\frac{22}{7}\). When 22 is divided by 7, the digits in the quotient after the decimal point are non-terminating and non-repeating, hence, pi is an irrational number. As a result, instead of the quotient, \(\frac{22}{7}\) is commonly used in everyday calculations, as the fractional form of pi.
Value of Pi(\(\pi\)) as a Decimal
The value of pi up to the first 10 decimal places is 3.1415926535. To simplify the calculation process, pi is usually taken as 3.14.
Formula for Pi
Pi is the ratio of a circle’s circumference to its diameter. Therefore, the formula is:
\(\pi=\frac{Circumference}{Diameter}\).
We know that the diameter is twice the radius.
Hence \(\pi\) can also be written as:
\(\pi=\frac{Circumference}{2~\times~radius}\)
Pi can also be defined as the ratio of the area of the circle to the square of its radius.
\(\pi=\frac{Area~ of~ Circle}{radius^2}\)
Solved Examples
Example 1:
What is the distance walked by a boy who walks around a circular park with a diameter of 200 m?
Solution:
Distance walked = Circumference of the circular park
\(Circumference=\pi~\times~diameter\)
\(=\pi~\times~200\)
= 628.318 m
As a result, the boy walked a distance of 628.318 m.
Example 2:
The diameter of a circle is 140 meter. Find the circumference of the circle.
Solution:
Given, the diameter of a circle is 280 meters.
\(C=\pi d\)
\(C=\left(\frac{22}{7}\right)~\times~280\)
= 880 m
The circumference of the circle is 880 meters.
Example 3:
Find the area of a circle with radius of 5 inches.
Solution:
\(A=\pi r^2\)
\(=3.14~\times~5^2\)
\(=3.14~\times~25\)
= 78.5 square inches
The area is 78.5 square inches.
The value of pi is used in a variety of formulas to calculate the area and circumference of a circle, the volume of cylinders, and other things. The value of pi is 3.14 or \(\frac{22}{7}\).
The digits after the decimal point in pi never end. These digits are non-recurring and non-terminating, and hence pi is an irrational number, which is roughly written as 3.14. Thus, the digits in pi will not terminate.
The circumference of a circle divided by its diameter is the formula for the value of pi. It’s written as \(\pi=\frac{Circumference}{Diameter}\).
The fractional representation of pi is \(\frac{22}{7}\). This value is used in formulas for easier calculation.