# Decimal system

For example:

4,309=(4×10^{3})+(3×10^{2})+(0×10^{1})+(9×10^{0})= 4×1,000+3×100+0×10+9×1,

and

4,309=(4×10^{0})+(3×10^{-1})+(0×10^{-2})+(9×10^{-3})= 4×1+3×0.1+0×0.01+9×0.001

It is believed that the decimal system is based on 10 because humans have 10 fingers and
so became used to counting by 10s early in the course of civilization. The decimal system
was introduced into Europe c.1300. It greatly simplified arithmetic and was a much-needed
improvement over the Roman numerals, which did not use a positional system. A number written
in the decimal system is called a decimal, although sometimes this term is used to refer only
to a proper fraction written in this system and not to a mixed number.
Decimals are added and subtracted in the same way as are integers (whole numbers) except that when
these operations are written in columnar form the decimal points in the column entries and in the
answer must all be placed one under another. In multiplying two decimals the operation is the same
as for integers except that the number of decimal places in the product, i.e., digits to the right
of the decimal point, is equal to the sum of the decimal places in the factors; e.g., the factor 7.24
to two decimal places and the factor 6.3 to one decimal place have the product 45.612 to three decimal
places. In division, e.g., 4.32/12.8 where there is a decimal point in the divisor (4.32), the
point is shifted to the extreme right (i.e., to 432.) and the decimal point in the dividend (12.8)
is shifted the same number of places to the right (to 1280), with one or more zeros added before
the decimal to make this possible. The decimal point in the quotient is then placed above that
in the dividend, i.e., 432/1280.0 Zeros are added to the right of the decimal point in the
dividend as needed, and the division proceeds the same as for integers. The decimal system is widely
used in various systems employing numbers. The metric system of weights and measures, used in most of
the world, is based on the decimal system, as are most systems of national currency.