# Decimal

**base 10decimal systemdecimal fractiondecimal fractionsbase-10base tendecimal notationdecimal number10decimal numeral system**

The decimal numeral system (also called base-ten positional numeral system, and occasionally called denary or decanary) is the standard system for denoting integer and non-integer numbers.wikipedia

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### 10

**ten10 (number)#10**

The decimal numeral system (also called base-ten positional numeral system, and occasionally called denary or decanary) is the standard system for denoting integer and non-integer numbers.

Ten is the base of the decimal numeral system, by far the most common system of denoting numbers in both spoken and written language.

### Positional notation

**positionalpositional numeral systemplace-value**

The decimal numeral system (also called base-ten positional numeral system, and occasionally called denary or decanary) is the standard system for denoting integer and non-integer numbers.

Positional notation (or place-value notation, or positional numeral system) denotes usually the extension to any base of the Hindu–Arabic numeral system (or decimal system).

### Hindu–Arabic numeral system

**Hindu-Arabic numeral systemHindu-Arabic numeralsHindu numerals**

It is the extension to non-integer numbers of the Hindu–Arabic numeral system.

The Hindu–Arabic numeral system or Indo-Arabic numeral system (also called the Arabic numeral system or Hindu numeral system) is a positional decimal numeral system, and is the most common system for the symbolic representation of numbers in the world.

### Numeral system

**numeralsnumeralnumeration**

The decimal numeral system (also called base-ten positional numeral system, and occasionally called denary or decanary) is the standard system for denoting integer and non-integer numbers.

For example, "11" represents the number eleven in the decimal numeral system (used in common life), the number three in the binary numeral system (used in computers), and the number two in the unary numeral system (e.g. used in tallying scores).

### Decimal separator

**decimal pointdecimal markthousands separator**

Decimals may sometimes be identified for containing a decimal separator (for example the "." For writing numbers, the decimal system uses ten decimal digits, a decimal mark, and, for negative numbers, a minus sign "−".

A decimal separator is a symbol used to separate the integer part from the fractional part of a number written in decimal form.

### Number

**number systemnumericalnumbers**

A tallying system has no concept of place value (as in modern decimal notation), which limits its representation of large numbers.

### Repeating decimal

**recurring decimalrepeatrepetend**

A repeating decimal is an infinite decimal that after some place repeats indefinitely the same sequence of digits (for example

Every terminating decimal representation can be written as a decimal fraction, a fraction whose divisor is a power of 10 (e.g. ); it may also be written as a ratio of the form k⁄2 n 5 m (e.g. ). However, every number with a terminating decimal representation also trivially has a second, alternative representation as a repeating decimal whose repetend is the digit 9.

### Numerical digit

**digitdigitsdecimal digit**

For writing numbers, the decimal system uses ten decimal digits, a decimal mark, and, for negative numbers, a minus sign "−".

The name "digit" comes from the fact that the ten digits (Latin digiti meaning fingers) of the hands correspond to the ten symbols of the common base 10 numeral system, i.e. the decimal (ancient Latin adjective decem meaning ten) digits.

### Roman numerals

**Roman numeralRomanRoman number**

Examples are Brahmi numerals, Greek numerals, Hebrew numerals, Roman numerals, and Chinese numerals.

Roman numerals are essentially a decimal or "base 10" number system, in that the powers of ten – thousands, hundreds, tens and units – are written separately, from left to right, in that order.

### Rational number

**rationalrational numbersrationals**

). An infinite decimal represents a rational number if and only if it is a repeating decimal or has a finite number of nonzero digits. The numbers that are represented by decimal numerals are the decimal fractions (sometimes called decimal numbers), that is, the rational numbers that may be expressed as a fraction, the denominator of which is a power of ten.

These statements hold true not just for base 10, but also for any other integer base (e.g. binary, hexadecimal).

### Real number

**realrealsreal-valued**

The decimal system has been extended to infinite decimals, for representing any real number, by using an infinite sequence of digits after the decimal separator (see Decimal representation).

In the 16th century, Simon Stevin created the basis for modern decimal notation, and insisted that there is no difference between rational and irrational numbers in this regard.

### Greek numerals

**Greek numeralGreeknumeric**

Examples are Brahmi numerals, Greek numerals, Hebrew numerals, Roman numerals, and Chinese numerals.

Greek numerals are decimal, based on powers of 10.

### Fraction (mathematics)

**denominatorfractionsfraction**

The numbers that may be represented in the decimal system are the decimal fractions, that is the fractions of the form The numbers that are represented by decimal numerals are the decimal fractions (sometimes called decimal numbers), that is, the rational numbers that may be expressed as a fraction, the denominator of which is a power of ten.

A decimal fraction is a fraction whose denominator is not given explicitly, but is understood to be an integer power of ten.

### Exponentiation

**exponentpowerpowers**

The numbers that are represented by decimal numerals are the decimal fractions (sometimes called decimal numbers), that is, the rational numbers that may be expressed as a fraction, the denominator of which is a power of ten.

In the base ten (decimal) number system, integer powers of

### 0.999...

**0.999…Proof that 0.999... equals 10.**

If all d n for n > N equal to 9 and [x] n = [x] 0 .d 1 d 2 ...d n, the limit of the sequence is the decimal fraction obtained by replacing the last digit that is not a 9, i.e.: d N, by d N + 1, and replacing all subsequent 9s by 0s (see 0.999...).

This repeating decimal represents the smallest number no less than every decimal number in the sequence (0.9, 0.99, 0.999, ...).

### Hexadecimal

**hex0x16**

For external use by computer specialists, this binary representation is sometimes presented in the related octal or hexadecimal systems.

Unlike the common way of representing numbers with ten symbols, it uses sixteen distinct symbols, most often the symbols "0"–"9" to represent values zero to nine, and "A"–"F" (or alternatively "a"–"f") to represent values ten to fifteen.

### Fractional part

**mod 1**

The part from the decimal separator to the right is the fractional part, which equals the difference between the numeral and its integer part.

For a positive number written in a conventional positional numeral system (such as binary or decimal), its fractional part hence corresponds to the digits appearing after the radix point.

### Decimal floating point

**decimal floating-pointDecimaldecimal arithmetic**

Often this arithmetic is done on data which are encoded using some variant of binary-coded decimal, especially in database implementations, but there are other decimal representations in use (including decimal floating point such as in newer revisions of the IEEE 754 Standard for Floating-Point Arithmetic).

Decimal floating-point (DFP) arithmetic refers to both a representation and operations on decimal floating-point numbers.

### Binary-coded decimal

**BCDbinary coded decimalpacked decimal**

Often this arithmetic is done on data which are encoded using some variant of binary-coded decimal, especially in database implementations, but there are other decimal representations in use (including decimal floating point such as in newer revisions of the IEEE 754 Standard for Floating-Point Arithmetic).

In computing and electronic systems, binary-coded decimal (BCD) is a class of binary encodings of decimal numbers where each decimal digit is represented by a fixed number of bits, usually four or eight.

### ENIAC

**Electronic Numerical Integrator And ComputerElectronic computerENIAC (Electronic Numerical Integrator and Computer)**

Most modern computer hardware and software systems commonly use a binary representation internally (although many early computers, such as the ENIAC or the IBM 650, used decimal representation internally).

Twenty of these modules were accumulators that could not only add and subtract, but hold a ten-digit decimal number in memory.

### IEEE 754

**IEEE floating-pointIEEE floating-point standardIEEE floating point**

Often this arithmetic is done on data which are encoded using some variant of binary-coded decimal, especially in database implementations, but there are other decimal representations in use (including decimal floating point such as in newer revisions of the IEEE 754 Standard for Floating-Point Arithmetic).

### Decimal representation

**decimal expansiondecimaldecimal expression**

The decimal system has been extended to infinite decimals, for representing any real number, by using an infinite sequence of digits after the decimal separator (see Decimal representation).

### Binary number

**binarybinary numeral systembase 2**

Most modern computer hardware and software systems commonly use a binary representation internally (although many early computers, such as the ENIAC or the IBM 650, used decimal representation internally).

The residents of the island of Mangareva in French Polynesia were using a hybrid binary-decimal system before 1450.

### Significant figures

**precisionsignificant digitssignificant digit**

In both cases, the true value of the measured quantity could be, for example, 0.0803 or 0.0796 (see also significant figures).

As an illustration, the decimal quantity 12.345 can be expressed with various numbers of significant digits or decimal places.

### Immanuel Bonfils

**Bonfils, Immanuel**

The Jewish mathematician Immanuel Bonfils used decimal fractions around 1350, anticipating Simon Stevin, but did not develop any notation to represent them.

1300 – 1377) was a French-Jewish mathematician and astronomer in medieval times who flourished from 1340 to 1377, a rabbi who was a pioneer of exponential calculus and is credited with inventing the system of decimal fractions.