[decimal]
In the decimal division method, sometimes it can be divided completely, that is, the decimal places of the quotient obtained are limited, for example, 1.26 ÷ 0.3 = 4.2; Sometimes there are endless situations. For example, calculate 10 ÷ 3. In this division method, because the remainder repeats 1, the quotient repeats 3, which can not be divided completely. So 10 ÷ 3 = 3. 333...... the number of digits of the quotient obtained by this division is infinite, and it is also written according to the bit value principle of the decimal system. Such a number is also called decimal.
The number of digits in the decimal part is a finite decimal, which is called a finite decimal.
[infinite decimal]
The number of digits in the decimal part is infinite decimal, which is called infinite decimal. There are two cases of infinite decimals: one is circular decimals, and the other is infinite non circular decimals, also known as irrational numbers.
A decimal, from a certain digit of the decimal part, a number or several numbers appear repeatedly. Such a decimal is called a circular decimal. In the decimal part of a circular decimal, the numbers that appear repeatedly in turn are called circular sections.
For example,
3.14949...... is a circular decimal and 49 is a circular section thereof;
0.888... Is a circular decimal, and 8 is a circular section of it;
The circular decimal from the first place after the decimal point in the circular section is called pure circular decimal. Circular decimals with one or more digits after the decimal point are called mixed circular decimals.
For example, 0.888, 4.3838, 7.128128 are pure circular decimals; 3.14848 and 0.03636 are mixed cycle decimals.
π (PI) is an infinite non cyclic decimal, which is about 3.141592654. On October 16, 2011, Maoli Kondo, an employee of the company in Iida City, Nagano Prefecture, Japan, calculated the PI to 10 trillion digits after the decimal point with his home computer.