For example, the result of converting 123456789 to an English numeral is as follows.
One Hundred Twenty-Three Million Four Hundred Fifty-Six Thousand Seven Hundred Eighty-Nine
Values after the decimal point can be expressed in word or fractional digits. For example, 0.99 is represented as "Zero point Nine Nine" in word and "Zero and 99/100" in fractions.
Large Numbers
For larger numbers, the digits are short scale or long scale and are expressed as follows: The name of the digit changes by 3 digits on the short scale and by 6 digits on the long scale. The long scale also has the Chuquet system, which represents digits of 106N+3 as "Thousand -illion", and the Peletier system, which represents "-illiard".
Short scale is mainly used in English-speaking countries such as the United States, Canada, and the United Kingdom (since 1974). In addition, the long scale Chuquet system was used in the United Kingdom before 1973, and the Peletier system is used in each language-specific notation in Europe, which is mainly non-English speaking countries such as France, Germany, and Italy.
DenCode uses the short scale that is common in modern English-speaking countries.
Short Scale
Long Scale (Chuquet)
Long Scale (Peletier)
Digit
N (103N+3)
Name
N (106N)
Name
N (106N)
Name
103
0
Thousand
0.5
Thousand
0.5
Thousand
106
1
Million
1
Million
1
Million
109
2
Billion
1.5
Thousand Million
1.5
Milliard
1012
3
Trillion
2
Billion
2
Billion
1015
4
Quadrillion
2.5
Thousand Billion
2.5
Billiard
1018
5
Quintillion
3
Trillion
3
Trillion
1021
6
Sextillion
3.5
Thousand Trillion
3.5
Trilliard
1024
7
Septillion
4
Quadrillion
4
Quadrillion
1027
8
Octillion
4.5
Thousand Quadrillion
4.5
Quadrilliard
1030
9
Nonillion
5
Quintillion
5
Quintillion
1033
10
Decillion
5.5
Thousand Quintillion
5.5
Quintilliard
1036
11
Undecillion
6
Sextillion
6
Sextillion
1039
12
Duodecillion
6.5
Thousand Sextillion
6.5
Sextilliard
1042
13
Tredecillion
7
Septillion
7
Septillion
1045
14
Quattuordecillion
7.5
Thousand Septillion
7.5
Septilliard
1048
15
Quindecillion
8
Octillion
8
Octillion
1051
16
Sexdecillion
8.5
Thousand Octillion
8.5
Octilliard
1054
17
Septendecillion
9
Nonillion
9
Nonillion
1057
18
Octodecillion
9.5
Thousand Nonillion
9.5
Nonilliard
1060
19
Novemdecillion
10
Decillion
10
Decillion
1063
20
Vigintillion
10.5
Thousand Decillion
10.5
Decilliard
The above digit names are common in current English dictionaries.
The name of the long scale Chuquet and Pelletier system was derived from French mathematician Nicolas Chuquet in 1484 defined until the "Nonillion" of N=9 (Byllion, Tryllion, Quadrillion, Quyllion, Sixlion, Septyllion, Ottyllion, and Nonyllion, in French), and Jacques Peletier du Mans spread "Milliard" (Milliart) in 1549 ("Milliard" was popularized in the sense of 1012 and Reduced to 109 later in the late 17th century).
Conway-Wechsler system
The Conway-Wechsler system defined by John Horton Conway and Allan Wechsler is a typical naming method for large digits with N=10 or more (1033 or more). The Conway-Wechsler system names digits according to the following rules:
Conway-Wechsler system
Units
Tens
Hundreds
1
un
(n) deci
(nx) centi
2
duo
(ms) viginti
(n) ducenti
3
tre (s(x))
(ns) triginta
(ns) trecenti
4
quattuor
(ns) quadraginta
(ns) quadringenti
5
quin(qua)
(ns) quinquaginta
(ns) quingenti
6
se (sx)
(n) sexaginta
(n) sescenti
7
septe (mn)
(n) septuaginta
(n) septingenti
8
octo
(mx) octoginta
(mx) octingenti
9
nove (mn)
nonaginta
nongenti
The Conway-Wechsler system was defined for short scales, but it can also be used for long scales. To get the digit name with this system, find the N of 103N+3 on the short scale and 106N on the long scale, and then use that N value to find the name in above table.
For example, 1096 is N=31 because it is 103*31+3 on the short scale, and it is combined from the lowest digit to the highest digit of N like "duo"(1) + "triginta"(30) + " illion" = "Duotrigintillion". If there is a vowel "aeiou" immediately before "illion", remove a vowel and combine them.
Also, when combining Units with Tens or Hundreds, the characters (mnsx) in parentheses in the above table are combined, including the characters if they match. This is called an assimilation rule. For example, for N=26, "se (sx)"(6) + "(ns) triginta"(20) + "illion" = "Sestrigintillion".
"tre (s(x))"(3) is special, and "s" is added regardless of which character follows (sx). For example, for N=83, It will be "tre (s(x))"(3) + "(mx) octoginta"(80) + "illion" = "Tresoctogintillion".
For more larger numbers with N=1,000 and above, combine N every 3 digits with the above procedure to derive the name and finally join. If N=1,000,000X + 1,000Y + Z and the name of each digit is "Xillion", "Yillion", "Zillion", they are combined like "Xilliyillizillion" and omit "on" of "-illion" in the middle. For example, if N=1,003, then "Million"(1) + "Trillion"(3) = "Millitrillion". Also, when N=12,210, "Duodecillion"(12) + "Deciducentillion"(210) = "Duodecillideciducentillion".
Also, if the 3-digit value is 0, it will be "Nillion". For example, if N=1,000,003, then "Million"(1) + "Nillion"(0) + "Trillion"(3) = "Millinillitrillion".
The Conway-Wechsler system is basically Latin-based, so for example the following names may differ from the names defined in the English dictionary.
N
Conway-Wechsler system
English dictionary
Latin word
15
Quinquadecillion
Quindecillion
5 is "quinque", but 15 is more commonly "quindecim" than "quinquadecim".
16
Sedecillion
Sexdecillion
"Sedecim" is more common than "sexdecim".
19
Novendecillion
Novemdecillion
Normally it is "undeviginti", but it may be written as "novendecim" or "novemdecim". A similar assimilation rule, N=17, is more commonly "septendecim" than "septemdecim".
The "quinqua" for 5 is "quinque" in Latin, but 15 is "quindecim" in Latin and "quindecillion" in English. Therefore, only "quinqua" in the Conway-Wechsler system may be replaced with "quin". This replacement was presented by Olivier Miakinen (See:Olivier Miakinen. Les zillions selon Conway, Wechsler... et Miakinen, 2003 (French web page)). DenCode also uses "quin", which is closer to the name of the English dictionary.
CW4EN system
DenCode supports the above Conway-Wechsler system, but it defines its own system that is more in line with the English dictionary and uses it as the default conversion system. For convenience, we will refer to it as "CW4EN system" (Conway-Wechsler for English system).
CW4EN system
Units
Tens
Hundreds
1
un
deci
(s) centi
2
duo
viginti
ducenti
3
tre (s)
triginta
trecenti
4
quattuor
quadraginta
quadringenti
5
quin
quinquaginta
quingenti
6
sex
sexaginta
sescenti
7
septen
septuaginta
septingenti
8
octo
octoginta
octingenti
9
novem
nonaginta
nongenti
"Tre (s(x))", "se (sx)", "septe (mn)", and "nove (mn)" of the Conway-Wechsler system are fixed at "tre", "sex", "septen", and "novem" on the CW4EN system. Only when N=103 is "Trescentillion" instead of "Trecentillion". This is to avoid duplication with "Trecentillion" with N=300.
There are examples of adopting systems similar to the CW4EN system, but they do not take into account or mention the difference between "Trescentillion" / "Trecentillion". (e.g. Glossary of Stock Market Terms & Definitions | Nasdaq)
The following is a list of typical names that differ between the Conway-Wechsler system and the CW4EN system.
N
Conway-Wechsler system
CW4EN system
16
Sedecillion
Sexdecillion
19
Novendecillion
Novemdecillion
23
Tresvigintillion
Trevigintillion
26
Sesvigintillion
Sexvigintillion
27
Septemvigintillion
Septenvigintillion
33
Trestrigintillion
Tretrigintillion
36
Sestrigintillion
Sextrigintillion
39
Noventrigintillion
Novemtrigintillion
43
Tresquadragintillion
Trequadragintillion
46
Sesquadragintillion
Sexquadragintillion
49
Novenquadragintillion
Novemquadragintillion
53
Tresquinquagintillion
Trequinquagintillion
56
Sesquinquagintillion
Sexquinquagintillion
59
Novenquinquagintillion
Novemquinquagintillion
66
Sesexagintillion
Sexsexagintillion
69
Novensexagintillion
Novemsexagintillion
76
Seseptuagintillion
Sexseptuagintillion
79
Novenseptuagintillion
Novemseptuagintillion
83
Tresoctogintillion
Treoctogintillion
87
Septemoctogintillion
Septenoctogintillion
96
Senonagintillion
Sexnonagintillion
97
Septenonagintillion
Septennonagintillion
99
Novenonagintillion
Novemnonagintillion
109
Novencentillion
Novemcentillion
206
Seducentillion
Sexducentillion
209
Novenducentillion
Novemducentillion
303
Trestrecentillion
Tretrecentillion
306
Sestrecentillion
Sextrecentillion
309
Noventrecentillion
Novemtrecentillion
403
Tresquadringentillion
Trequadringentillion
406
Sesquadringentillion
Sexquadringentillion
409
Novenquadringentillion
Novemquadringentillion
503
Tresquingentillion
Trequingentillion
506
Sesquingentillion
Sexquingentillion
509
Novenquingentillion
Novemquingentillion
606
Sesescentillion
Sexsescentillion
609
Novensescentillion
Novemsescentillion
706
Seseptingentillion
Sexseptingentillion
709
Novenseptingentillion
Novemseptingentillion
803
Tresoctingentillion
Treoctingentillion
807
Septemoctingentillion
Septenoctingentillion
906
Senongentillion
Sexnongentillion
907
Septenongentillion
Septennongentillion
909
Novenongentillion
Novemnongentillion
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