# Numerals

A numeral is a symbol used to represent a number. Numerals are made up of digits; 1 is a digit, "123" is made up of 3 digits, and "123" is a numeral that represents the number one hundred twenty-three (note that "one hundred twenty-three" is also a numeral). There are many different ways to represent the same number using various numerals, as shown below for the number 8.

Examples

With a digit | : | 8 |

With the addition operation | : | 5 + 3 |

With the division operation | : | 16 ÷ 2 |

With Roman numerals | : | VIII |

With tally marks | : | llll ll |

## Numeral vs number

The terms number and numeral are often used interchangeably, but they are technically not the same thing.

A number is a mathematical object used for counting and measurement. Numerals are the symbols used to represent numbers. For example, if John has 5 cookies, he can indicate this by writing the number "5," the word "five," the roman numeral "V," or he can hold up 5 of his fingers. There are many different ways to express the number of cookies that John has using various numerals, but all of the numerals still mean that he has 5 cookies.

## Decimal numeral system

A numeral system is a set of rules and symbols used to represent numbers. The most commonly used numeral system is the Hindu-Arabic numeral system, a positional numeral system that uses the numerals 1, 2, 3, 4, 5, 7, 8 and 9.

The decimal numeral system is an extension of the Hindu-Arabic numeral system that includes non-integer numbers. In the decimal numeral system, each digit in a numeral has a place value.

For example, the numeral "2" represents the number two. On the other hand, the numeral "222" represents the number two hundred twenty-two. Each of the digits is the same, but in the numeral 222, each of the 2s has a different value. The left-most 2 is in the hundreds place, the middle 2 is in the tens place, and the right-most 2 is in the ones place. Their value is determined by what position they are in, which is referred to as their place value. The numeral 222 can be expanded as follows:

222 = 2 × 10^{2} + 2 × 10^{1} + 2 × 10^{0}

222 = 2 × 100 + 2 × 10 + 2× 1

222 = 200 + 20 + 2

In the decimal numeral system, negative numbers are indicated using a negative sign (-), and a decimal point (.) is used to separate the integer portions of a numeral from the decimal portions. For example, negative two hundred twenty-two and two tenths is written as: -222.2.