Table of Contents

## Value of Pi

The ratio of a circle’s circumference to its diameter, or Pi, has a value that is nearly equivalent to 3.14159. In a circle, the result of dividing the circumference (the total distance encircling the circle) by the diameter is always the same. The value of pi is constant regardless of the size of the circle. Pi is represented by the symbol, which is pronounced: “pie.” It serves as a symbol for a mathematical constant and is the 16th letter in the Greek alphabet.

## What is the Value of Pi in Decimals and Fractions?

The Value of Pi (or π) is mainly expressed in two different ways

- Value of Pi in Decimal.
- Value of Pi in Fraction.

## Value of Pi in Decimal

Since pi is an irrational number, as was already mentioned, there are infinite decimal places following the number 3. The digits from 0 to 9 make up the 100 decimal places of pi. There are twelve 2s, eleven 3s, ten 4s, eight 5s, nine 6s, eight 7s, twelve 8s, and fourteen 9s. There are also eight 0s and eight 1s. Look at the illustration below, which demonstrates that the decimal representation of pi begins with 3 and ends with the number 9.

The pi value up to the first 100 decimal places is:

3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679

## Value of Pi in Fraction

22/7 is the pi fractional value. It is well known that Pi is an irrational number, meaning that the decimal place is followed by an infinite amount of digits, making Pi a non-terminating value. As a result, 22/7 is used in common calculations. ” this is an irrational number since it cannot be expressed as the ratio of any two numbers.

All Values of Pi (π) | |
---|---|

In Decimal | 3.14 |

In Fraction | 22⁄7 |

## Pi Value is 22/7

## Formula of Pi Value

By dividing a circle’s circumference by its diameter, one may determine pi. Since the circumference of a circle is proportional to its diameter, the formula for computing pi is:

**π = Circumference/Diameter**

“How I wish I could calculate pi” is a clever way to help us remember the value of pi. We can quickly write the value of pi by calculating how many letters are contained in each word. Since “How” has three letters, “I” has one, “want” has four, “I” has one, “could” has five, “calculate” has nine, and “pi” has two. Consequently, 3.141592 is the estimated value of pi to six decimal digits.

## Value of Pi in Degrees and Angles in Trigonometry

Since 180° in radians is equal to pi in degrees, the value of pi in degrees equals 180°. We shall examine the idea of radians, the SI unit for measuring angles, in order to comprehend this. We are aware that one full rotation of a circle equals its circumference. It indicates that if we revolve 360° around a fixed point (the circle’s center) at a fixed distance (its radius), we will obtain the circumference, which is equal to 2r, where r stands for the circle’s radius. Circumference = 2 r = 360 degrees can therefore be written. Additionally, for a half-circle, the angle is 180° and the arc’s length is 2r/2, which equals r. 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 degrees is 180 degrees.

## Value of pi by 2

The Value of pi by 2 is 1.571 in Radians and 90° in Degrees.

## Value of pi by 4

The Value of pi by 4 is 0.785 in Radians and 45° in Degrees.

## Value of pi square

The Value of pi square is 9.8596 in Radians.

## π values

Degrees | Radians (exact) |
Radians (approx) |
---|---|---|

30° | π/6 | 0.524 |

45° | π/4 | 0.785 |

60° | π/3 | 1.047 |

90° | π/2 | 1.571 |

180° | π | 3.142 |

270° | 3π/2 | 4.712 |

360° | 2π | 6.283 |

## How to calculate the value of Pi?

To calculate the value of π, the pi formula is used, which is:

π = (Circumference/ Diameter)

Or, π = 3.14159 = 22/7

## Value of Pi Examples

**Question 1: **A girl walks around a circle which has a diameter of 200 m, how far the girl has walked?

**Solution:**

Distance walked = Circumference.

Circumference = π × 200m = 628 m

Therefore, distance walked = 628 m

**Question** **2:** Calculate the circumference of the circle.

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 substituting the value of d, we get;

C = π x 20

=3.14 x 20

= 62.8 cm

## Value of Pi: Important points

- The reciprocal of the ratio of a circle’s circumference to its diameter is known as “Pi” in mathematics.
- It is an irrational number that is frequently calculated as 3.14159.
- Based on the issue, we use pi as 22/7, or 3.14, to simplify calculations.
- Here are a few simple pi-based circle formulas:
- Area = π
^{2}and Circumference = Diameter.

## Value of Pi in Maths QNAs

**Que. What is the value of Pi?**

Ans. The values of Pi are 3.14 and 22/7.

**Que. What is the entire number of pi?**

Ans. 3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679

**Que. Which country value is Pi?**

Ans. T**he Egyptians** calculated the area of a circle by a formula that gave the approximate value of 3.1605 for π.

**Que. Who invented the Pi in India?**

Ans. Aryabhata invented Pi in India.

**Que. Why is 3.14 called Pi?**

Ans. It was first called “Pi” in 1706 by [the Welsh mathematician] William Jones because pi is the first letter in the Greek word perimitros, which means “perimeter.”