Decimals are introduced as follows:
Decimal is a special expression of real numbers. All fractions can be expressed as decimals, and the points in decimals are called decimal points, which are the dividing lines between the integer part and the decimal part of a decimal. Decimals with zero integer parts are called pure decimals, and decimals with non-zero integer parts are called decimals.
Finite decimals are introduced as follows:
A decimal with a finite number of digits after the decimal part. For example, 3. 1465, 0.364, 8.32 18798456, etc. All finite decimals belong to rational numbers and can be converted into component numbers.
A simplest fraction can be converted into a decimal finite fraction if and only if its denominator contains only prime factors 2 or 5 or both. Similarly, a simplest fraction can be transformed into a finite fraction of the base of a positive integer if and only if the prime factor of its denominator is a subset of the prime factor of the base.
The decimal point is introduced as follows:
Decimal point, a mathematical symbol written as ".",is used to separate the integer part from the decimal part in decimal system. Although the decimal point is small, it plays a great role.
China has used decimal counting method since ancient times, and some practical units of measurement also use decimal, so it is easy to produce the concept of decimal.
The first person to express this concept in words was Liu Hui in Wei and Jin Dynasties. In the process of calculating pi, he used seven units, such as feet, inches, minutes, centimeters, millimeters, seconds and bumps. For the following units that suddenly become smaller, they are no longer named and collectively referred to as decimals.
In Europe and Islamic countries, sexagesimal of Babylon has been in a dominant position for a long time, and some classic scientific works have also adopted sexagesimal, so the concept of decimal has never been developed.
/kloc-Alkasi in Central Asia in the 0/5th century (? ~ 1429) is the first person to use decimals outside China. European mathematicians didn't start to consider decimals until16th century, among which Steven (1548 ~ 1620), a Dutchman, clearly expressed this point in his book Decimal System (1583).