Numerals in Unicode
Numerals (often called numbers in Unicode) are characters or sequences of characters that denote a number. The same ArabicIndic numerals are used widely in various writing systems throughout the world and all share the same semantics for denoting numbers. However, the graphemes representing these numerals differ widely from one writing system to another. To support these grapheme differences, Unicode includes encodings of these numerals within many of the script blocks. The decimal digits are repeated in 23 separate blocks: twice in Arabic. Six additional blocks contain the digits again as rich text primarily to serve as a palette of graphemes for specialized mathematical use. In addition to many forms of the ArabicIndic numerals, Unicode also includes several less common numerals such as: Aegean numerals, Roman numerals, counting rod numerals, Cuneiform numerals and ancient Greek numerals.
Numerals invariably involve composition of glyphs as a limited number of characters are composed to make other numerals. For example, the sequence 9–9–0 in ArabicIndic numerals composes the numeral for nine hundred ninety (990). In Roman numerals, the same number is expressed by the composed numeral Ⅹↀ or ⅩⅯ. Each of these is a distinct numeral for representing the same abstract number. The semantics of the numerals differ in particular in their composition. The ArabicIndic decimal digits are positionalvalue compositions, while the Roman numerals are signvalue and they are additive and subtractive depending on their composition.
Numerals by numeric property
Grouped by their numerical property as used in a text, Unicode has four values for Numeric Type. First there is the "not a number" type. Then there are decimalradix numbers, commonly used in Western style decimals (plain 09), there are numbers that are not part of a decimal system such as Roman numbers, and decimal numbers in typographic context, such as encircled numbers. Not noted is a numbering like "A. B. C." for chapter numbering.
Numeric Type^{[a]}^{[b]} (Unicode character property)  

Numeric type  Code  Has Numeric Value  Example  Remarks 
Not numeric  None  No 

Numeric Value="NaN" 
Decimal  De  Yes 

Straight digit (decimalradix). Corresponds both ways with General Category=Nd^{[a]} 
Digit  Di  Yes 

Decimal, but in typographic context 
Numeric  Nu  Yes 

Numeric value, but not decimalradix 
a. ^ "Section 4.6: Numeric Value" (PDF). The Unicode Standard. Unicode Consortium. July 2016.  
b. ^ "Unicode 9.0 Derived Numeric Types". Unicode Character Database. Unicode Consortium. 20160302. 
Hexadecimal digits
Hexadecimal digits in Unicode are not separate characters, existing letters and numbers are used. These characters have marked Character properties Hex_digit=Yes
, and ASCII_Hex_digit=Yes
when appropriate.
Characters in Unicode marked Hex_Digit=Yes ^{[a]}  

0123456789ABCDEF  Basic Latin, capitals  Also ASCII_Hex_Digit=Yes  
0123456789abcdef  Basic Latin, small letters  Also ASCII_Hex_Digit=Yes  
０１２３４５６７８９ＡＢＣＤＥＦ  Fullwidth forms, capitals  
０１２３４５６７８９ａｂｃｄｅｆ  Fullwidth forms, small letters  
a. ^ "Unicode 9.0 UCD: PropList.txt". 20160601. Retrieved 20160621. 
Numerals by script
Arabic–Indic numerals
The Arabic–Indic numerals involve ten digits (for base ten; 0–9 ) and a decimal separator that can be combined into composite numerals representing any rational number. Unicode includes these ten digits in the Basic Latin (or ASCII derived) block. Unicode has no decimal separator for common unified use. The Arabic script includes an Arabic specific decimal separator (U+066B). Other writing systems are to use whatever punctuation produces the appropriate glyph for the locale: for example ‘Full Stop’ (U+002E period) in United States usage and Comma (U+002C) in many other locales.
The Arabic–Indic digits are repeated in several other scripts: Arabic, Balinese, Bengali, Devanagari, Ethiopic, Gujarati, Gurmukhi, Telugu, Khmer, Lao, Limbu, Malayalam, Mongolian, Myanmar, New Tai Lue, Nko, Oriya, Telugu, Thai, Tibetan, Osmanya. Unicode includes a numeric value property for each digit to assist in collation and other text processing operations. However, there is no mapping between the various related Arabic–Indic digits.
Fractions
The fraction slash character (U+2044) allows authors using Unicode to compose any arbitrary fraction along with the decimal digits. Unicode also includes a handful of vulgar fractions as compatibility characters, but discourages their use.
Decimal fractions
Several characters in Unicode can serve as a decimal separator depending on the locale. Decimal fractions are represented in text as a sequence of decimal digit numerals with a decimal separator separating the wholenumber portion from the fractional portion. For example, the decimal fraction for “¼” is expressed as zeropointtwofive (“0.25”). Unicode has no dedicated general decimal separator but unifies the decimal separator function with other punctuation characters. So the “.” used in “0.25” is the same period character used to end the sentence. However, cultures vary in the glyph or grapheme used for a decimal separator. So in some locales, the comma may be used instead ”0,25”. Still other locales use a space for “0 25”. The Arabic writing system includes a dedicated character for a decimal separator that looks much like a comma ”٫” (U+066B) which when combined with the Arabic graphemes for the Arabic–Indic decimal digits to express onequarter appears as: “٠٫٢٥”.
Note that although Arabic is written from right to left, while English is written left to right, in both languages numbers are written with the most significant digit on the left and the least significant on the right.
Characters for mathematical constants
Currently, three Unicode characters semantically represent mathematical constants: U+210E ℎ PLANCKS CONSTANT, the U+210F ℏ REDUCED PLANCK CONSTANT, and U+2107 ℇ EULER CONSTANT. Other mathematical constants can be represented using characters that have multiple semantic uses. For example, although Unicode includes a character for natural exponent ℯ (U+212F) its UCS canonical name derives from its glyph: U+212F ℯ SCRIPT SMALL E; and the mathematical constant π, 3.141592.., is represented by U+03C0 π GREEK SMALL LETTER PI.
Rich text and other compatibility numerals
The Arabic–Indic numerals also appear among the compatibility characters as rich text variant forms including bold, doublestruck, monospace, sansserif and sansserif bold. and fullwidth variants for legacy vertical text support.
Rich text parenthesized, circled and other variants are also included in the blocks: Enclosed CJK Letters and Months; Enclosed Alphanumerics, Superscripts and Subscripts; Number Forms; and Dingbats.
CJK Suzhou (huāmǎ) numerals
The huāmǎ system is a variation of the rod numeral system. Rod numerals are closely related to the counting rods and the abacus, which is why the numeric symbols for 1, 2, 3, 6, 7 and 8 in the huāmǎ system are represented in a similar way as on the abacus. Nowadays, the huāmǎ system is only used for displaying prices in Chinese markets or on traditional handwritten invoices.
Suzhou (huāmǎ) numerals in Unicode
According to the Unicode standard version 3.0, these characters are called Hangzhou style numerals. This indicates that it is not used only by Cantonese in Hong Kong. In the Unicode standard 4.0, an erratum was added which stated:
The digits of the Suzhou numerals are designated in the CJK Symbols and Punctuation block between U+3021 and U+3029, U+3007, U+5341, U+5344, and. U+5345.
Japanese and Korean numerals
Ancient Greek numerals
Unicode provides support for several variants of Greek numerals, assigned to the Supplementary Multilingual Plane from U+10140 through U+1018F.^{[1]}
Attic numerals were used by ancient Greeks, possibly from the 7th century BC. They were also known as Herodianic numerals because they were first described in a 2ndcentury manuscript by Herodian. They are also known as acrophonic numerals because all of the symbols used derive from the first letters of the words that the symbols represent: 'one', 'five', 'ten', 'hundred', 'thousand' and 'ten thousand'. See Greek numerals and acrophony.
Decimal  Symbol  Greek numeral 

1  Ι  ἴος or ἰός (ios) 
5  Π  πέντε (pente) 
10  Δ  δέκα (deka) 
100  Η  ἑκατόν (hekaton) 
1000  Χ  χίλιοι (khilioi) 
10000  Μ  μύριοι (myrioi) 
Ancient Greek Numbers^{[1]}^{[2]} Official Unicode Consortium code chart (PDF)  
0  1  2  3  4  5  6  7  8  9  A  B  C  D  E  F  
U+1014x  𐅀  𐅁  𐅂  𐅃  𐅄  𐅅  𐅆  𐅇  𐅈  𐅉  𐅊  𐅋  𐅌  𐅍  𐅎  𐅏 
U+1015x  𐅐  𐅑  𐅒  𐅓  𐅔  𐅕  𐅖  𐅗  𐅘  𐅙  𐅚  𐅛  𐅜  𐅝  𐅞  𐅟 
U+1016x  𐅠  𐅡  𐅢  𐅣  𐅤  𐅥  𐅦  𐅧  𐅨  𐅩  𐅪  𐅫  𐅬  𐅭  𐅮  𐅯 
U+1017x  𐅰  𐅱  𐅲  𐅳  𐅴  𐅵  𐅶  𐅷  𐅸  𐅹  𐅺  𐅻  𐅼  𐅽  𐅾  𐅿 
U+1018x  𐆀  𐆁  𐆂  𐆃  𐆄  𐆅  𐆆  𐆇  𐆈  𐆉  𐆊  𐆋  𐆌  𐆍  𐆎  
Notes 
Roman numerals
Roman numerals are a numeral system originating in ancient Rome, adapted from Etruscan numerals. The system used in classical antiquity was slightly modified in the Middle Ages to produce the system we use today. It is based on certain letters which are given values as numerals.
Roman numerals are commonly used today in numbered lists (in outline format), clockfaces, pages preceding the main body of a book, chord triads in music analysis (Roman numeral analysis), the numbering of movie and video game sequels, book publication dates, successive political leaders or children with identical names, and the numbering of some sport events, such as the Olympic Games or the Super Bowl.
Roman numerals in Unicode
Unicode has a number of characters specifically designated as Roman numerals, as part of the Number Forms^{[2]} range from U+2160 to U+2188. This range includes both upper and lowercase numerals, as well as precombined characters for numbers up to 12 (Ⅻ or XII). One reason for the existence of precombined numbers is to facilitate the setting of multipleletter numbers (such as VIII) on a single horizontal line in Asian vertical text. The Unicode standard, however, includes special Roman numeral code points for compatibility only, stating that "[f]or most purposes, it is preferable to compose the Roman numerals from sequences of the appropriate Latin letters".^{[3]}
Additionally, characters exist for archaic^{[2]} forms of 1000, 5000, 10,000, large reversed C (Ɔ), late 6 (ↅ, similar to Greek Stigma: Ϛ), early 50 (ↆ, similar to down arrow ↓⫝⊥^{[4]}), 50,000, and 100,000. Note that the small reversed c, ↄ is not intended to be used in Roman numerals, but as lower case Claudian letter Ↄ,
Code x=  0  1  2  3  4  5  6  7  8  9  A  B  C  D  E  F 

Value^{[5]}  1  2  3  4  5  6  7  8  9  10  11  12  50  100  500  1,000 
U+216x  Ⅰ  Ⅱ  Ⅲ  Ⅳ  Ⅴ  Ⅵ  Ⅶ  Ⅷ  Ⅸ  Ⅹ  Ⅺ  Ⅻ  Ⅼ  Ⅽ  Ⅾ  Ⅿ 
U+217x  ⅰ  ⅱ  ⅲ  ⅳ  ⅴ  ⅵ  ⅶ  ⅷ  ⅸ  ⅹ  ⅺ  ⅻ  ⅼ  ⅽ  ⅾ  ⅿ 
Value  1000  5000  10,000  –  –  6  50  50,000  100,000  
U+218x  ↀ  ↁ  ↂ  Ↄ  ↄ  ↅ  ↆ  ↇ  ↈ 
If using blackletter or script typefaces, Roman numerals are set in Roman type. Such typefaces may contain Roman numerals matching the style of the typeface in the Unicode range U+2160–217F; if they don't exist, a matching Antiqua typeface is used for Roman numerals.
Unicode has characters for Roman fractions in the Ancient Symbols^{[6]} block: sextans, uncia, semuncia, sextula, dimidia sextula, siliqua, and as.
Countingrod numerals
Value  0  1  2  3  4  5  6  7  8  9 

Vertical  
Horizontal 
The vertical rods are usually for even powers of ten (1, 100, 10000...) and the horizontal for odd powers (10, 1000...). For example, 126 is represented by instead of , which could be confused with 36. Historically, red rods were used for positive numbers and black rods for negative numbers.
Counting rod numerals in Unicode
Counting rod numerals are included in their own block in the Supplementary Multilingual Plane (SMP) from U+1D360 to U+1D37F. Eighteen characters for vertical and horizontal digits of 19 are included as of Unicode 5.0, though vertical and horizontal are opposite from the description above. Fourteen code points reserved for future use. Zero should be represented by U+3007 (〇, ideographic number zero) and the negative sign should be represented by U+20E5 (combining reverse solidus overlay).^{[7]} As these were recently added to the character set and since they are included in the SMP, font support may still be limited.
Counting Rod Numerals^{[1]}^{[2]} Official Unicode Consortium code chart (PDF)  
0  1  2  3  4  5  6  7  8  9  A  B  C  D  E  F  
U+1D36x  𝍠  𝍡  𝍢  𝍣  𝍤  𝍥  𝍦  𝍧  𝍨  𝍩  𝍪  𝍫  𝍬  𝍭  𝍮  𝍯 
U+1D37x  𝍰  𝍱  
Notes 
See also
 Number Forms (Unicode block)
References
 ↑ Unicode Charts: Ancient Greek Numbers
 1 2 Unicode Number Forms
 ↑ The Unicode Standard, Version 6.0 – Electronic edition (PDF), Unicode, Inc., 2011, p. 486
 ↑ David J. Perry: Proposal to Add Additional Ancient Roman Characters to UCS
 ↑ For the first two rows
 ↑ Unicode Ancient Symbols
 ↑ The Unicode Standard, Version 5.0 – Electronic edition (PDF), Unicode, Inc., 2006, pp. 499–500