Value of Pi
The value of pi is the ratio of the circumference of a circle to its diameter. The pi symbol is denoted as π. It is also called Archimedes' constant which was named after the Greek mathematician, Archimedes, who created an algorithm to approximate the pi value. The value of pi is irrational, which means that the count of digits after the decimal point is infinite. It is used as either 3.1415929 or 22/7. In geometry, it is used in calculating the surface area, volume, and circumference of various three-dimensional shapes.
What is the Value of Pi?
The value of 'pi' is constant, which means it cannot be changed. It is an irrational number usually approximated to 3.14. It is used in various formulas for the measurement of surface area and volume of various solid shapes. 'Pi' is defined as the ratio of the circumference of the circle to the diameter of the circle. We know that the diameter of a circle is the longest line segment that passes through the center of the circle. Imagine the line of diameter is bent such that it covers a part of the circumference of the circle. Now, π is defined as the total number of times the diameter is wrapped around the circumference of the circle which is 3.14 times approximately.
If we divide the circumference by the diameter, we get approximately 3.14. It should be noted that no matter what size of a circle we draw, the ratio of the circumference to its diameter will always be the same.
Symbol for Pi
The symbol used to denote pi in math is π, which is used in Greek letters. It is known as a mathematical constant as its value does not change. The pi symbol represents 22/7 in fractions or 3.14 (approximately) in decimals.
Formula for Pi
The value of pi can be obtained by dividing the circumference of a circle by its diameter. Since pi is the ratio of the circumference of a circle to its diameter, the formula for calculating π is:
π = Circumference/Diameter
One interesting statement that helps us to remember the value of pi is "How I wish I could calculate pi". By counting the number of letters in each word, we can easily write the value of pi. Since 'How' has 3 letters; 'I' - 1 letter, 'wish' - 4 letters, 'I' - 1 letter, 'could' - 5 letters, 'calculate' - 9 letters, 'pi' - 2 letters. Therefore, the value of pi approximated to 6 decimal places is 3.141592.
How to Calculate the Value of Pi?
The value of pi can be calculated with the help of a simple activity. Follow the steps given below to know why the value of pi is the ratio of the circumference to the diameter of the circle:
- Step 1: Draw a circle of diameter 1 unit.
- Step 2: After this step, take a thread and place it along the border of the circle (the circumference).
- Step 3: Now, place the thread on the ruler and note the length.
Repeat the process with diameters of 2 units, 3 units, 4 units, 5 units, and record your observations in the table.
| Diameter | Circumference | Circumference/Diameter |
|---|---|---|
| 1 unit | 3.1 units | 3.1/1 |
| 2 units | 6.2 units (approx.) | 6.2/2 = 3.1 |
| 3 units | 9.3 units (approx.) | 9.3/3 = 3.1 |
| 4 units | 12.4 units (approx.) | 12.4/4 = 3.1 |
| 5 units | 15.5 units (approx.) | 15.5/5 = 3.1 |
We can observe that the ratio of circumference to diameter is always the same which is 3.1.
Value of Pi in Decimals
As discussed above, the value of pi is an irrational number, which means there are infinite decimal places after the number 3. The 100 decimal places of pi consist of all digits from 0 to 9. There are eight 0s, eight 1s, twelve 2s, eleven 3s, ten 4s, eight 5s, nine 6s, eight 7s, twelve 8s, and fourteen 9s. Observe the figure given below which shows that the value of pi in decimals starts with 3 and the 100th decimal digit holds the number 9.
The value of pi in decimals is non-terminating and non-recurring and is approximated to 100 decimal places as 3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679. For ease of calculations, it is often approximated to 3.14.
Value of Pi in Fraction
The value of pi in fraction is 22/7. We know that the value of pi is an irrational number in which the digits after the decimal point are infinite. Therefore, to make calculations easier the value of pi is also defined in the form of a fraction and is expressed as 22/7.
Value of Pi in Degree
The value of pi in degree is 180 degrees, as π radians is equal to 180°. To understand this, we will be looking at the concept of radians which is the SI unit of measuring angles. We know that in a circle, one complete revolution makes the circumference of the circle. It means if we rotate by 360° around a point (known as the center of the circle) at a fixed distance (radius), we will get the circumference, which is equal to 2πr, where r denoted the radius of the circle. So, we can write, Circumference = 2πr = 360 degrees. And, for half a circle, the angle is 180° and the length of the arc will be 2πr/2 = πr. The formula of radians is arc length/radius. So, for half a circle, the arc length is πr and the radius is r.
⇒ πr/r radians = 180°
⇒ π radians = 180°
Therefore, the value of pi in degree is 180 degrees.
Important Notes:
Some important points about the pi symbol and value are given below:
- 'Pi' is a mathematical constant that is the ratio of the circumference of a circle to its diameter. It is an irrational number often approximated to 3.14159.
- Based on the problem, for ease of calculation, we use the value of pi as 22/7 or 3.14.
- A few basic circle formulas using pi are,
a) Circumference = π × Diameter
b) Area = πr2
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FAQs on Value of Pi
What is Pi in Math?
Pi, in mathematics, is a constant which is the ratio of the circumference of a circle to its diameter. It is an irrational number often approximated to 3.14159. It is denoted by the Greek letter 'π' and is spelled as 'pie'. Sometimes, to ease the calculation, the value of pi is used in the form of a fraction as 22/7.
What does the Pi Symbol mean?
The pi symbol is denoted as 'π' which is a Greek alphabet. The pi symbol is mostly used to calculate the circumference of circles, surface area, and volume of three-dimensional shapes.
What is the Value of Pi?
The value of pi is equal to 3.1415929.. or 22/7. It is an irrational number which means that the decimal places after 3 are never-ending. The value of pi is extensively used in the concepts of measurement of surface area, the volume of 3D shapes, etc.
What are the First 100 Digits of Pi Value?
The first 100 digits of pi are 3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679. The value of pi starts with a 3 followed by a decimal point. Since pi is an irrational number, the digits after the decimal point are infinite. The 100th digit after the decimal point is 9.
Does the Value of Pi Ever End?
The pi value never ends because it is an irrational number. It is a non-terminating and non-recurring number which is approximately written as 3.14. The number of decimal places after the decimal point extends up to infinity.
Why is the Value of Pi Important?
The value of pi is important due to the following reasons:
- Pi, in mathematics, is used to calculate the area and circumference of circles.
- π is used in many formulas in trigonometry to examine the relationship between the lengths and angles of triangles and in geometry where we study shapes, sizes, relative positions, and the properties of space.
- It is also used extensively in the field of architecture and robotics.
- Pi (π) is considered very important, hence, March 14 is celebrated as 'Pi day' to recognize this constant.
What is the Pi Formula?
The formula for the value of pi is the ratio of the circumference of a circle to its diameter. In the ratio form, it is represented as π = Circumference/Diameter.
What is Pi used for?
The value of pi is used in various formulas that are used to calculate the area and circumference of a circle, the volume of cylinders, and so on. The value of pi is given as 3.14 or 22/7.
How was the Value of Pi Discovered?
The value of pi was discovered by dividing the circumference of a circle by the diameter. This ratio which is approximately equal to 3.14 remains the same even if the diameter or the circumference of a circle changes. The ancient Babylonians and Egyptians calculated the value of pi for practical purposes. Then, around 250 BC, a Greek mathematician created an algorithm for it. Later, the value was approximated by the Chinese mathematicians up to seven digits and then up to five digits.
How to Find the Value of Pi?
The value of pi is calculated by dividing the circumference of a circle by its diameter. A simple activity shown below can prove that the ratio or value of pi remains the same even if the diameter and the circumference change.
- Step 1: Draw a circle of diameter 1 unit.
- Step 2: After this step, take a thread and place it along the border of the circle (the circumference).
- Step 3: Now, place the thread on the ruler and note the length.
- Step 4: Repeat the process with diameters of 2 units, 3 units, 4 units, 5 units, and record your observations in a table. We can observe that the ratio of circumference to diameter is always the same which is 3.1:1.
What is the Value of Pi in Degree?
The value of pi in degrees is equal to 180°. Here the concept of radian will help us understand this. Radian is the SI unit for measuring angles. One radian is defined as the angle that is subtended from the center of a circle that intercepts an arc that is equal in length to the radius of the given circle. The magnitude of one complete revolution (360°) in radians is the length of the circumference divided by the radius or 2πr/ r = 2π. Therefore, 2π (radians) = 360°, which gives, π = 180°.
What is the Value of Pi in Fraction?
The value of pi in the form of a fraction is 22/7. This value is used in formulas for easier calculation.
What are the Two Ways in which we can use the Value of Pi?
The value of pi can be used as 3.1415929 or 22/7 based on the convenience for calculation of certain measurements like surface areas and volume. Both the values give the same result. For radian to degree conversion, the value of π radians is equal to 180 degrees.