What is Pi?
Pi is an irrational number, it is the ratio of the circumference of the circle to its diameter. The pi symbol is 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 the count of numbers after the decimal places is infinite. The value of pi is used as either 3.1415929 or 22/7. The pi symbol is used in calculating the surface area, volume, and circumference of three-dimensional shapes.
|1.||What is Pi in Math?|
|2.||Formula for Pi|
|3.||How to Calculate Pi?|
|4.||100 Decimal Place of Pi|
|7.||FAQs on Value of Pi|
What is Pi in Math?
The value of 'pi' is constant, which means it cannot be changed. It is an irrational number usually approximated to 3.14. It is denoted by the symbol 'π'. 'Pi' is used in various formulas in 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. Let us understand this. 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. This can be clearly understood from the figure shown below.
Formula for Pi
Now that we have understood what is pi, and we have observed that the pi value is constant, let us see how to calculate it. The value of pi can be obtained by dividing the circumference of the circle by its diameter. Pi is the ratio of the circumference of a circle to its diameter. The formula for calculating π is:
π = Circumference/Diameter
One important 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. pi number approximated to 6 decimal place is 3.141592.
How to Calculate Pi?
One of the easiest methods to calculate the diameter of a circle is to use a thread wrapped around the circumference of the circle. Let us do a small activity to see how to calculate pi. By the end of this activity, we will know what is pi exactly. Follow the steps given below to know why the value of pi is the ratio of the circumference of the circle to the diameter of the circle.
Step 1: Draw a circle of diameter 1 units.
Step 2: Now, 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.
|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.
100 Decimal Places of Pi
As discussed already, the value of pi is an irrational number, which means there are infinite numbers 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. We can observe from the figure below that the value of pi starts with 3 and the 100th decimal digit holds the number 9.
The value of pi is an irrational number. Value of pi is non-terminating and non-recurring. Pi value approximated to 100 decimal places is 3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679. For ease of calculations, it is often approximated to 3.14.
Some important points about the pi symbol 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, use the value of pi as 22/7 or 3.14
- Basic circle formula with pi is,
a)Circumference = π × Diameter units
b)Area = πr2 square units
Topics Related to What is pi
Check out some interesting topics related to pi.
Solved Examples on pi Value
Example 1: A pizza of a diameter of 14 units is divided into 6 equal parts. What is the area of one slice of the pizza? (Use the value of pi as 22/7).
We know that radius = diameter/2.
Given diameter = 14 units.
radius = 14/2
= 7 units
Since the pizza is of circular shape, we can use the formula for the area of a circle to calculate the area of the pizza.
Area of the circle = πr2
Substituting the value of π and radius in the formula, we get,
Area = 22/7 × 7 × 7
= 22 × 7
= 154 square units.
Therefore, area of one slice of the pizza = Area of the pizza/number of slices.
= 25.66 square units,
Therefore, the area of a slice of pizza = 25.66 square units.
Example 2: John had to replace a leaky pipe. He measured 44 units as the circumference of the pipe. What is the diameter of the pipe he should buy? Use the value of pi as 22/7.
The circumference of the given pipe is 44 units.
Therefore, 2πr = 44
2 × 22/7 × r = 44
44 × r = 44 × 7
r = (44 × 7)/44
r = 7 units
Diameter = 2 × radius
= 2 × 7
= 14 units.
Therefore, the diameter of the pipe = 14 units.
Example 3: Betty measured the diameter and circumference of a hula loop accurately. The diameter was 113 units and the circumference was 355 units. She used these measurements and found the value of pi. Is her value close to the real value of pi?
We know that π = Circumference/Diameter
Given, circumference = 355 units and diameter = 113 units.
Therefore, the value of pi (π) = 355/113
Therefore, 355/113 is very close to the pi value.
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'. It is spelled as 'pie'.
What is Pi Symbol?
What is the Value of Pi?
The value of pi is equal to 3.1415929 or 22/7. The value of pi is an irrational number. It 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?
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.
Will the Value of Pi Ever End?
The pi value will never end. It is an irrational number. It is a non-terminating and non-recurring number. 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. They are,
- Pi in maths is used to calculate the area and circumference of circles.
- Any circular shape is dependent on the pi value.
- π is found in many formulae 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 and hence, March 14 is celebrated as Pi day.
What is the Formula to Find the Value of Pi?
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 π = Circumference/Diameter.
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 of them give the same result.
Is the Value of pi the Same for any Circumference and Diameter of a Circle?
As the diameter of a circle increases, the circumference also increases. But the ratio of circumference to the diameter which is the value of pi is always the same.
List Out Some Important Formulas That Uses the Value of Pi.
Some important formulas that use the value of pi are as follows.
- Area of circle = πr2, where 'r' is the radius
- Circumference of circle = π × Diameter
- Volume of a cylinder = πr2h, where 'r' is the radius and 'h' is the height of the cylinder.