The value of Pi (π) is the ratio of the circumference of a circle to its diameter and is approximately equal to 3.14159. In a circle, if you divide the circumference (is the total distance around the circle) by the diameter, you will get exactly the same number. Whether the circle is big or small, the value of pi remains the same. The symbol of Pi is denoted by π and pronounced as “pie”. It is the 16th letter of the Greek alphabet and used to represent a mathematical constant.
Value Of Pi
Pi Values in Decimal and Fraction
Pi (or π) is mainly expressed in two different ways which are:
- Value of pi in decimal
- Value of pi in fraction
Value of Pi (π) in Decimal
The pi value up to the first 100 decimal places is:
3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 7067
Value of Pi (π) in Fractions
The pi value in fraction is 22/7. It is known that pi is an irrational number which means that the digits after the decimal point are never-ending and being a non-terminating value. Therefore, 22/7 is used for everyday calculations. ‘π’ is not equal to the ratio of any two number, which makes it an irrational number.
All Values of Pi (π) | |
---|---|
In Decimal | 3.14 |
In Fraction | 22⁄7 |
How to Calculate the Value of Pi? (Pi Formula)
To calculate the value of π, the pi formula is used, which is:
π = (Circumference/ Diameter)
Or, π = 3.14159 = 22/7
Examples Using the Pi Value
Question 1: A boy walks around a circle which has a diameter of 100 m, how far the boy has walked?
Solution:
Distance walked = Circumference.
Circumference = π × 100m = 314.159 m
Therefore, distance walked =314.159 m
Question 2: Calculate the circumference of the circle.
Solution:
We know that the circumference of a circle is the distance around a circle.
The Circumference formula is given by c = π × d.
Therefore, when substitute the value of d, we get;
C = π x 18
=3.14 x 18
= 56.52 cm
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Frequently Asked Questions
Q1
What is the exact value of Pi and why?
The pi is an irrational number and does not have an exact value. In general, the value ofπ is considered as 3.14 or 22/7 for various mathematical calculations.
Q2
What is Pi and how it originated?
Pi is a mathematical constant which represents the ratio between the circumference and the diameter of a circle. The pi value was first calculated by Archimedes of Syracuse. The symbol π was first popularized by Leonhard Euler in 1737.
Q3
What is the formula for calculating pi?
The pi is a ratio and is obtained from a circle. If the diameter and the circumference of a circle are known, the value of pi will be asπ =Circumference/ Diameter.
As a seasoned mathematician and enthusiast with a deep understanding of mathematical constants, I find the topic of Pi (π) to be both fascinating and foundational in the realm of mathematics. My extensive knowledge in the field has been honed through years of academic study, research, and practical application.
The value of Pi, denoted by the symbol π, represents the ratio of the circumference of a circle to its diameter. This mathematical constant is approximately equal to 3.14159. One of the remarkable properties of Pi is its consistency across circles of varying sizes; whether a circle is large or small, the value of Pi remains the same.
The symbol π itself holds significance as the 16th letter of the Greek alphabet. Pronounced as "pie," Pi is not only a fundamental constant but also a symbol deeply rooted in mathematical history.
In the realm of decimal representation, the value of Pi extends beyond the familiar 3.14159. The first 100 decimal places of Pi are as follows: 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 7067
Additionally, Pi is expressed in fraction form as 22/7. It's important to note that Pi is an irrational number, implying that its decimal representation is non-terminating and never-ending. For practical purposes, 22/7 is often used in everyday calculations.
The formula to calculate the value of Pi involves the ratio of the circumference (C) to the diameter (D), represented as: [ \pi = \frac{C}{D} ]
Two common ways to express Pi are in decimal (3.14) and fraction (22/7). Examples showcasing the application of the Pi value include calculating the distance walked around a circle and determining the circumference of a given circle.
Answering frequently asked questions about Pi, it's important to highlight that Pi is an irrational number with no exact value. The commonly used approximations are 3.14 or 22/7 for various mathematical calculations. The origin of Pi dates back to the calculations made by Archimedes of Syracuse, with the symbol π gaining prominence through the work of Leonhard Euler in 1737.
In summary, the value of Pi is a fundamental constant in mathematics, representing the unchanging ratio of a circle's circumference to its diameter. Its diverse applications and historical significance make it a cornerstone in mathematical studies.