This article is about different methods of expressing numerals in the English language for children with symbols. For the classification of numbers in mathematics, see Number system.
This article includes a list of references, but its sources remain unclear because it has insufficient inline citations. The number the numeral represents is called its value. Reflect the algebraic and arithmetic structure of the numbers. For example, the usual decimal representation of whole numbers gives every nonzero whole number a unique representation as a finite sequence of digits, beginning with a non-zero digit. Numeral systems are sometimes called number systems, but that name is ambiguous, as it could refer to different systems of numbers, such as the system of real numbers, the system of complex numbers, the system of p-adic numbers, etc.
Two Indian mathematicians are credited with developing it. The simplest numeral system is the unary numeral system, in which every natural number is represented by a corresponding number of symbols. Tally marks represent one such system still in common use. The unary notation can be abbreviated by introducing different symbols for certain new values. This system is used when writing Chinese numerals and other East Asian numerals based on Chinese. In English, one could say “four score less one”, as in the famous Gettysburg Address representing “87 years ago” as “four score and seven years ago”.
More elegant is a positional system, also known as place-value notation. Note that zero, which is not needed in the other systems, is of crucial importance here, in order to be able to “skip” a power. Arabic numeral system, which originated in India and is now used throughout the world, is a positional base 10 system. The positional decimal system is presently universally used in human writing. This is the meaning of the common notation 1,000,234,567 used for very large numbers.