What is meaning of pai decimal expansion

Thread starter sciboudy
Start date Mar 4, 2012
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decimal expansion Expansion

In summary, "pai" or "pi" is a mathematical constant representing the ratio of a circle's circumference to its diameter, approximated to 3.14. Its decimal expansion is used to accurately calculate its value and is essential in representing the infinite number of decimal digits. Pai's decimal expansion is considered irrational because it continues infinitely without any pattern or repetition. Understanding it is crucial in various fields of mathematics and scientific and technological development.

Mar 4, 2012

sciboudy

what is meaning of pai decimal expansion ?

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Mar 4, 2012

Office_Shredder

Staff Emeritus

Science Advisor

Gold Member

I think you're going to need to clarify your question. And by pai, do you mean pi?

Related to What is meaning of pai decimal expansion

1. What is the significance of "pai" in decimal expansion?

The term "pai" refers to the mathematical constant, also known as "pi", which represents the ratio of a circle's circumference to its diameter. It is commonly approximated to 3.14 and has infinite decimal digits in its expansion.

2. How is decimal expansion used to calculate the value of pai?

Decimal expansion is used to represent the value of pai in a base-10 system, where each digit represents a specific power of 10. This allows for the accurate calculation of pai to a desired number of decimal places.

3. What is the significance of the decimal point in pai's expansion?

The decimal point in pai's expansion indicates the separation between the whole number part and the fractional part of the number. It is essential for representing the infinite number of digits in pai's decimal expansion.

4. Why is pai's decimal expansion considered "irrational"?

Pai's decimal expansion is considered "irrational" because it cannot be expressed as a finite or repeating decimal. This means that the digits in its expansion continue infinitely without any pattern or repetition.

5. What is the importance of understanding pai's decimal expansion in mathematics?

Understanding pai's decimal expansion is crucial in mathematics as it is used in various formulas and equations related to geometry, trigonometry, and physics. It also plays a significant role in the development of numerical methods and algorithms used in scientific and technological fields.