desimaalikehitelmä

A desimaalikehitelmä, or decimal expansion, is a way of representing a real number using a base-10 positional numeral system. It consists of an integer part and a fractional part, separated by a decimal point. The integer part is written to the left of the decimal point, and the fractional part is written to the right. Each digit in the fractional part represents a multiple of a decreasing power of ten. For example, in the number 12.345, the '1' represents 10, the '2' represents 2, the '3' represents three-tenths (3/10), the '4' represents four-hundredths (4/100), and the '5' represents five-thousandths (5/1000).

Decimal expansions can be terminating or non-terminating. A terminating decimal expansion has a finite number of non-zero digits after the decimal point, such as 0.5 or 3.14. Non-terminating decimal expansions have an infinite number of digits after the decimal point. These can be further classified into repeating and non-repeating. A repeating decimal expansion has a sequence of digits that repeats indefinitely, such as 1/3 which is 0.333... or 1/7 which is 0.142857142857.... A non-repeating, non-terminating decimal expansion, such as that of pi (3.14159265...) or the square root of 2 (1.41421356...), has no repeating pattern and is characteristic of irrational numbers. The concept of decimal expansion is fundamental in arithmetic, calculus, and various branches of mathematics and science.