The name of the decimal system was put forward by Zhu Shijie, an algebraic scientist of the13rd generation. In the 13th century, lowercase symbols representing decimals appeared in China. In the west, decimals appear very late. It was not until the16th century that the French mathematician kravis first used the decimal point as a symbol to distinguish the integer part from the decimal part.

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.

Decimal nature:

Add or delete any zeros at the end of the decimal part, and the size of the decimal remains the same. For example: 0.4=0.400, 0.060=0.06. Move the decimal point to the right (or left) by n bits respectively, and the value of the decimal point will be expanded (or reduced) by n times.

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.

A number or numbers that start from somewhere in the decimal part and appear repeatedly in turn are called cyclic decimals. Cyclic decimals also belong to rational numbers and can be converted into component numbers.

There are infinite numbers in the decimal part. Decimals in which one number or several numbers do not appear repeatedly in turn are called infinite acyclic decimals, which are also irrational numbers and cannot be converted into numbers.