|
The English Name of a Number
How high can you count?
You can count as high as you want.
All you need to know some words, some prefixes and a few rules.
You may obtain the
Name
of a Number:
<<== Try this link!!
... and then come back :-)
Modern British or Traditional European?
No, we are not talking about swallows! :-)
Most English speakers
are able to count up to 999999999 (109-1)
using the just 31 words.
They can string them together to name a number such as 987654321:
nine hundred eighty seven million,
six hundred fifty four thousand,
three hundred twenty one
At 109, English forks into several number systems.
The English names of larger numbers such as
109 and 1012 depends on
which system you are using:
| Table 0 |
| Formal system name |
USA and Modern British
short scale |
Traditional European
long scale |
Traditional British
long scale |
| short system name |
American |
European |
British |
| 1 (100) |
one |
one |
one |
| 1000 (103) |
one thousand |
one thousand |
one thousand |
| 1000000 (106) |
one million |
one million |
one million |
| 1000000000 (109) |
one billion |
one millard |
one thousand million |
| 1000000000000 (1012) |
one trillion |
one billion |
one billion |
| 1000000000000000 (1015) |
one quadrillion |
one billiard |
one thousand billion |
| 1000000000000000000 (1018) |
one quintillion |
one trillion |
one trillion |
The name one milliard
is almost never seen in the USA and is rarely seen in
the UK except in older documents.
However it is frequently seen in Continental Europe.
For this reason we give the Traditional European long scale
system the short name of the European system.
Using one billion for 1000000000 (109) has been
common in the US for some time.
In 1974, Prime Minister Harold Wilson announced in the House of Commons
that the official meaning of one billion would change to
1000000000 (109) in conformity with usage in the US.
For this reason we give the USA and Modern British short scale
system the short name of the American system.
Prior to 1974, one billion in the UK was sometimes referred to
109
and sometimes
1012.
Many English speaking
peoples of the Commonwealth equate one billion with
1012.
For this reason we give the Traditional British long scale
system the short name of the British system.
We first describe counting in USA and Modern British short scale or
American system.
Later, we will address counting in the European and
British systems.
Before we get going, just a brief note about exponential notation:
1063 means 10 to the power of 63.
It is equal to the number 1 followed by 63 zeros:
1000000000000000000000000000000000000000000000000000000000000000
And 100021 means 1000 to the power of 21.
It is equal to the number 1 followed by 3*21 = 63 zeros,
which is the same value.
Starting to count
With the following 31 words, we able to count up to
999999999:
zero
one two three four five six seven eight nine
ten eleven twelve thirteen fourteen fifteen sixteen seventeen eighteen nineteen
twenty thirty forty fifty sixty seventy eighty ninety hundred
thousand million
We can string them together to name a number such as 987654321:
nine hundred eighty seven million,
six hundred fifty four thousand,
three hundred twenty one
Medium size numbers < 1063
To form names of numbers up to 1063-1, one needs the following:
zero
one two three four five six seven eight nine
ten eleven twelve thirteen fourteen fifteen sixteen seventeen eighteen nineteen
twenty thirty forty fifty sixty seventy eighty ninety hundred
thousand million
in addition to the following names:
| Table 1 |
| Formal system name |
USA and Modern British
short scale |
Traditional European
long scale |
Traditional British
long scale |
| short system name |
American |
European |
British |
| 109 = 10003 |
billion |
milliard |
thousand milliard |
| 1012 = 10004 |
trillion |
billion |
billion |
| 1015 = 10005 |
quadrillion |
billiard |
thousand billion |
| 1018 = 10006 |
quintillion |
trillion |
trillion |
| 1021 = 10007 |
sextillion |
trilliard |
thousand trillion |
| 1024 = 10008 |
septillion |
quadrillion |
quadrillion |
| 1027 = 10009 |
octillion |
quadrilliard |
thousand quadrillion |
| 1030 = 100010 |
nonillion |
quintillion |
quintillion |
| 1033 = 100011 |
decillion |
quintilliard |
thousand quintillion |
| 1036 = 100012 |
undecillion |
sextillion |
sextillion |
| 1039 = 100013 |
duodecillion |
sextilliard |
thousand sextillion |
| 1042 = 100014 |
tredecillion |
septillion |
septillion |
| 1045 = 100015 |
quattuordecillion |
septilliard |
thousand septillion |
| 1048 = 100016 |
quindecillion |
octillion |
octillion |
| 1051 = 100017 |
sexdecillion |
octilliard |
thousand octillion |
| 1054 = 100018 |
septendecillion |
nonillion |
nonillion |
| 1057 = 100019 |
octodecillion |
nonilliard |
thousand nonillion |
| 1060 = 100020 |
novemdecillion |
decillion |
decillion |
| 1063 = 100021 |
vigintillion |
decilliard |
thousand decillion |
Large size numbers < 10303
Most dictionaries, encyclopedias and reference works will list
names for numbers that stop just short of 100011 or
perhaps 100021.
However there is no reason to stop at this point!
Take a look at the American system for the moment in the above
table.
The prefix that is in front of "llion" is derived from something
called the Latin
cardinal number which is one less than something we call
a Latin power.
The term Latin power refers to the exponent of 1000.
So 10004 has a Latin power of 4.
The prefix cardinal is one less than the Latin power,
so 10004 has a prefix cardinal of 3.
The names for the Latin powers up thru 10 are special.
You just have to memorize them because the rules do
not become stable until the Latin power of 11.
Here are the names for the Latin powers 3 to 10:
| Table 2 |
| Number |
Latin Power |
prefix cardinal |
prefix |
American system
with dashes |
| 109 = 10003 |
3 |
2 |
bi |
bi-llion |
| 1012 = 10004 |
4 |
3 |
tri |
tri-llion |
| 1015 = 10005 |
5 |
4 |
quadri |
quadri-llion |
| 1018 = 10006 |
6 |
5 |
quinti |
quinti-llion |
| 1021 = 10007 |
7 |
6 |
sexti |
sexti-llion |
| 1024 = 10008 |
8 |
7 |
septi |
septi-llion |
| 1027 = 10009 |
9 |
8 |
octi |
octi-llion |
| 1030 = 100010 |
10 |
9 |
noni |
noni-llion |
Observe what happens to the next 10 Latin powers:
| Table 3 |
| Number |
Latin Power |
prefix cardinal |
prefix |
American system
with dashes |
| 1033 = 100011 |
11 |
10 |
dec |
dec-illion |
| 1036 = 100012 |
12 |
1 and 10 |
un dec |
un-dec-illion |
| 1039 = 100013 |
13 |
2 and 10 |
duo dec |
duo-dec-llion |
| 1042 = 100014 |
14 |
3 and 10 |
tre dec |
tre-dec-illion |
| 1045 = 100015 |
15 |
4 and 10 |
quattuor dec |
quattuor-dec-illion |
| 1048 = 100016 |
16 |
5 and 10 |
quin dec |
quin-dec-illion |
| 1051 = 100017 |
17 |
6 and 10 |
sex dec |
sex-dec-illion |
| 1054 = 100018 |
18 |
7 and 10 |
septen dec |
septen-dec-illion |
| 1057 = 100019 |
19 |
8 and 10 |
octo dec |
octo-dec-illion |
| 1060 = 100020 |
20 |
9 and 10 |
novem dec |
novem-dec-illion |
Note that the Latin power 18 turns into the prefix cardinal 7 and 10,
not 17.
The rules in Latin for forming numbers require us to say 7 and 10
instead of 17.
Here are the names for the Latin Powers 21 thru 30:
| Table 4 |
| Number |
Latin Power |
prefix cardinal |
prefix |
American system
with dashes |
| 1063 = 100021 |
21 |
20 |
vigin |
vigin-tillion |
| 1066 = 100022 |
22 |
1 and 20 |
un vigin |
un-vigin-tillion |
| 1069 = 100023 |
23 |
2 and 20 |
duo vigin |
duo-vigin-tillion |
| 1072 = 100024 |
24 |
3 and 20 |
tre vigin |
tre-vigin-tillion |
| 1075 = 100025 |
25 |
4 and 20 |
quattuor vigin |
quattuor-vigin-tillion |
| 1078 = 100026 |
26 |
5 and 20 |
quin vigin |
quin-vigin-tillion |
| 1081 = 100027 |
27 |
6 and 20 |
sex vigin |
sex-vigin-tillion |
| 1084 = 100028 |
28 |
7 and 20 |
septen vigin |
septen-vigin-tillion |
| 1087 = 100029 |
29 |
8 and 20 |
octo vigin |
octo-vigin-tillion |
| 1090 = 100030 |
30 |
9 and 20 |
novem vigin |
novem-vigin-tillion |
In the above table you will note that
Latin powers 21 to 30 use "vigin-" instead of "dec-".
Also note that the suffix changed from "-illion" to
"-tillion".
Using this set of 10 Latin power pattern, one need only know the
names of every tenth Latin power starting at 11:
| Table 5 |
| Number |
Latin Power |
prefix cardinal |
prefix |
American system
with dashes |
| 1033 = 100011 |
11 |
10 |
dec |
dec-illion |
| 1063 = 100021 |
21 |
20 |
vigin |
vigin-tillion |
| 1093 = 100031 |
31 |
30 |
trigin |
trigin-tillion |
| 10123 = 100041 |
41 |
40 |
quadragin |
quadragin-tillion |
| 10153 = 100051 |
51 |
50 |
quinquagin |
quinquagin-tillion |
| 10183 = 100061 |
61 |
60 |
sexagin |
sexagin-tillion |
| 10213 = 100071 |
71 |
70 |
septuagin |
septuagin-tillion |
| 10243 = 100081 |
81 |
80 |
octogin |
octogin-tillion |
| 10273 = 100091 |
91 |
90 |
nonagin |
nonagin-tillion |
Within a given set of 10 Latin powers, we need these prefixes:
| Table 6 |
| prefix cardinal |
prefix |
multiple
of 10 |
none |
| 1 and |
un |
| 2 and |
duo |
| 3 and |
tre |
| 4 and |
quattuor |
| 5 and |
quin |
| 6 and |
sex |
| 7 and |
septen |
| 8 and |
octo |
| 9 and |
novem |
Here is the rule for which suffix to use:
- For Latin powers 0, 1 and 2, there is no suffix
- For Latin powers 3 thru 10, the suffix is llion
- If the prefix ends in "dec", then the suffix is illion
(i.e., the Latin power mod 100 is 10 thru 19)
- Otherwise the suffix is tillion
Here are a few examples of numbers that can be formed with the two
tables above:
| Table 7 |
| Number |
Latin Power |
prefix cardinal |
prefix |
American system
with dashes |
| 1024 = 10008 |
8 |
7 |
septi |
septi-llion |
| 1033 = 100011 |
11 |
10 |
dec |
dec-illion |
| 1045 = 100015 |
15 |
4 and 10 |
quattuor dec |
quattuor-dec-illion |
Looking closely at the last entry in the table above (1015):
The Latin power of 15 gives us the Prefix cardinal of
"4 and 10".
Why? Well, the Prefix cardinal is one less than the Latin power.
We are required to write 14 as "4 and 10".
From Table 6 we find that the prefix for 4
is quattuor.
From Table 5 we find that the prefix for 10
is dec.
So the prefix for "4 and 10" is quattuor dec
Now because the prefix ends in "dec" we use the suffix illion.
Therefore the number 100015
(1000000000000000000000000000000000000000000000),
in the American system, has the name one quattuordecillion.
Here are a few more examples of some larger numbers:
| Table 8 |
| Number |
Latin Power |
prefix cardinal |
prefix |
American system
with dashes |
| 1063 = 100021 |
21 |
20 |
vigin |
vigin-tillion |
| 10150 = 100050 |
50 |
9 and 40 |
novem quadragin |
novem-quadragin-tillion |
| 10153 = 100051 |
51 |
50 |
quinquagin |
quinquagin-tillion |
| 10156 = 100052 |
52 |
1 and 50 |
un quinquagin |
un-quinquagin-tillion |
| 10222 = 100074 |
74 |
3 and 70 |
tre septuagin |
tre-septuagin-tillion |
| 10300 = 1000100 |
100 |
9 and 90 |
novem nonagin |
novem-nonagin-tillion |
Again looking closely at the last entry in the table above (1000100):
The Latin power of 100 gives us the Prefix cardinal of
"9 and 90".
Why? Well, the Prefix cardinal is one less than the Latin power.
We are required to write 99 as "9 and 90".
From Table 6 we find that the prefix for 9
is novem.
From Table 5 we find that the prefix for 90
is nonagin.
So the prefix for 4 and 10 is novem nonagin
Now because the prefix does NOT end in "dec" we use the suffix
tillion.
So the number 10300 = 1000100
in the American system, has the name one novemnonagintillion.
Now lets try naming a few numbers.
To avoid confusion between systems
that use decimal points in place of decimal commas,
we will put a space between sets of 3 digits.
To avoid confusion, the number
123456789246801357 will be written as:
123 456 789 246 801 357
Using the system described thus far, we are now able to convert the number into
multiples of Latin powers:
123 * 10005 (Latin power 5 = prefix cardinal 4 = quadri-llion)
456 * 10004 (Latin power 4 = prefix cardinal 3 = tri-llion)
789 * 10003 (Latin power 3 = prefix cardinal 2 = bi-llion)
246 * 10002 (Latin power 2 = prefix cardinal 1 = mi-llion)
801 * 10001 (thousand - special case)
357 * 10000 (units - special case)
The American system would name that number:
one hundred twenty three quadrillion,
four hundred fifty six trillion,
seven hundred eighty nine billion,
two hundred forty six million,
eight hundred one thousand,
three hundred fifty seven
Let us form the name of a larger number:
123 456 789 246 801 357 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
Using the system described thus far, we are now able to convert the number into
multiples of Latin powers:
123 * 100073 (Latin power 73 =
prefix cardinal 2 and 70 =
duo-septuagin-tillion)
456 * 100072 (Latin power 72 =
prefix cardinal 1 and 70 =
un-septuagin-tillion)
789 * 100071 (Latin power 71 =
prefix cardinal 70 =
septuagin-tillion)
246 * 100070 (Latin power 70 =
prefix cardinal 9 and 60 =
novem-sexagin-tillion)
801 * 100069 (Latin power 69 =
prefix cardinal 8 and 60 =
octo-sexagin-tillion)
357 * 100068 (Latin power 68 =
prefix cardinal 7 and 60 =
septen-sexagin-tillion)
Therefore,
the American system would name that number:
one hundred twenty three duoseptuagintillion,
four hundred fifty six unseptuagintillion,
seven hundred eighty nine septuagintillion,
two hundred forty six novemsexagintillion,
eight hundred one octosexagintillion,
three hundred fifty seven septensexagintillion
Gigantic size numbers < 103003
You may recall that the rules for Latin powers 0 to 10 were special.
Well there is a slightly special case for 100 to 109 as well.
This slightly special case applies to the first 9
Latin powers beyond a multiple of 100.
Here are the names of the numbers with Latin powers 100 to 109:
| Table 9 |
| Number |
Latin Power |
prefix cardinal |
prefix |
American system
with dashes |
| 10303 = 1000101 |
101 |
100 |
cen |
cen-tillion |
| 10306 = 1000102 |
102 |
100 1 |
cen un |
cen-un-tillion |
| 10309 = 1000103 |
103 |
100 2 |
cen duo |
cen-duo-tillion |
| 10312 = 1000104 |
104 |
100 3 |
cen tre |
cen-tre-tillion |
| 10315 = 1000105 |
105 |
100 4 |
cen quattuor |
cen-quattuor-tillion |
| 10318 = 1000106 |
106 |
100 5 |
cen quin |
cen-quin-tillion |
| 10321 = 1000107 |
107 |
100 6 |
cen sex |
cen-sex-tillion |
| 10324 = 1000108 |
108 |
100 7 |
cen septen |
cen-septen-tillion |
| 10327 = 1000109 |
109 |
100 8 |
cen octo |
cen-octo-tillion |
| 10330 = 1000110 |
110 |
100 9 |
cen novem |
cen-novem-tillion |
For Latin powers 110 to 119, the change of suffix rule
applies because we again end with "dec":
| Table 10 |
| Number |
Latin Power |
prefix cardinal |
prefix |
American system
with dashes |
| 10333 = 1000111 |
111 |
100 10 |
cen dec |
cen-dec-illion |
| 10336 = 1000112 |
112 |
100 1 and 10 |
cen un dec |
cen-un-dec-illion |
| 10339 = 1000113 |
113 |
100 2 and 10 |
cen duo dec |
cen-duo-dec-illion |
| 10342 = 1000114 |
114 |
100 3 and 10 |
cen tre dec |
cen-tre-dec-illion |
| 10345 = 1000115 |
115 |
100 4 and 10 |
cen quattuor dec |
cen-quattuor-dec-illion |
| 10348 = 1000116 |
116 |
100 5 and 10 |
cen quin dec |
cen-quin-dec-illion |
| 10351 = 1000117 |
117 |
100 6 and 10 |
cen sex dec |
cen-sex-dec-illion |
| 10354 = 1000118 |
118 |
100 7 and 10 |
cen septen dec |
cen-septen-dec-illion |
| 10357 = 1000119 |
119 |
100 8 and 10 |
cen octo dec |
cen-octo-dec-illion |
| 10360 = 1000120 |
120 |
100 9 and 10 |
cen novem dec |
cen-novem-dec-illion |
To name numbers with a Latin power beyond 100, we need the following table:
| Table 11 |
| Number |
Latin Power |
prefix cardinal |
prefix |
American system
with dashes |
| 10303 = 1000101 |
101 |
100 |
cen |
cen-tillion |
| 10603 = 1000201 |
201 |
200 |
duocen |
duocen-tillion |
| 10903 = 1000301 |
301 |
300 |
trecen |
trecen-tillion |
| 101203 = 1000401 |
401 |
400 |
quadringen |
quadringen-tillion |
| 101503 = 1000501 |
501 |
500 |
quingen |
quingen-tillion |
| 101803 = 1000601 |
601 |
600 |
sescen |
sescen-tillion |
| 102103 = 1000701 |
701 |
700 |
septingen |
septingen-tillion |
| 102403 = 1000801 |
801 |
800 |
octingen |
octingen-tillion |
| 102703 = 1000901 |
901 |
900 |
nongen |
nongen-tillion |
Let us form the name of an even larger number:
123 456 789 246 801 357 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
Using the system described thus far, we are now able to convert the number into
multiples of Latin powers:
123 * 1000173 (Latin power 173 =
prefix cardinal 100 2 and 70 =
cen-duo-septuagin-tillion)
456 * 1000172 (Latin power 172 =
prefix cardinal 100 1 and 70 =
cen-un-septuagin-tillion)
789 * 1000171 (Latin power 171 =
prefix cardinal 100 70 =
cen-septuagin-tillion)
246 * 1000170 (Latin power 170 =
prefix cardinal 100 9 and 60 =
cen-novem-sexagin-tillion)
801 * 1000169 (Latin power 169 =
prefix cardinal 100 8 and 60 =
cen-octo-sexagin-tillion)
357 * 1000168 (Latin power 168 =
prefix cardinal 100 7 and 60 =
cen-septen-sexagin-tillion)
Observe that the 100's prefix comes before the units and tens prefix.
In the American system, that number would be named:
one hundred twenty three cenduoseptuagintillion,
four hundred fifty six cenunseptuagintillion,
seven hundred eighty nine censeptuagintillion,
two hundred forty six cennovemsexagintillion,
eight hundred one cenoctosexagintillion,
three hundred fifty seven censeptensexagintillion
Going 200 Latin powers larger:
123 456 789 246 801 357 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
Using the system described thus far, we are now able to convert the number into
multiples of Latin powers:
123 * 1000373 (Latin power 373 =
prefix cardinal 300 2 and 70 =
trecen-duo-septuagin-tillion)
456 * 1000372 (Latin power 372 =
prefix cardinal 300 1 and 70 =
trecen-un-septuagin-tillion)
789 * 1000371 (Latin power 371 =
prefix cardinal 300 70 =
trecen-septuagin-tillion)
246 * 1000370 (Latin power 370 =
prefix cardinal 300 9 and 60 =
trecen-novem-sexagin-tillion)
801 * 1000369 (Latin power 369 =
prefix cardinal 300 8 and 60 =
trecen-octo-sexagin-tillion)
357 * 1000368 (Latin power 368 =
prefix cardinal 300 7 and 60 =
trecen-septen-sexagin-tillion)
In the American system, we would say:
one hundred twenty three trecenduoseptuagintillion,
four hundred fifty six trecenunseptuagintillion,
seven hundred eighty nine trecenseptuagintillion,
two hundred forty six trecennovemsexagintillion,
eight hundred one trecenoctosexagintillion,
three hundred fifty seven trecenseptensexagintillion
Titanic size numbers < 103000003
When we reach titanic numbers, we need a new prefix:
| Table 12 |
| Number |
Latin Power |
prefix cardinal |
prefix |
American system
with dashes |
| 103003 = 10001001 |
1001 |
1000 |
millia |
millia-tillion |
Lets look at a titanic number example:
123 456 789 246 801 357 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
We can convert that number into multiples of Latin powers:
123 * 10001073 (Latin power 1073 =
prefix cardinal thousand 2 and 70 =
millia-duo-septuagin-tillion)
456 * 10001072 (Latin power 1072 =
prefix cardinal thousand 1 and 70 =
millia-un-septuagin-tillion)
789 * 10001071 (Latin power 1071 =
prefix cardinal thousand 70 =
millia-septuagin-tillion)
246 * 10001070 (Latin power 1070 =
prefix cardinal thousand 9 and 60 =
millia-novem-sexagin-tillion)
801 * 10001069 (Latin power 1069 =
prefix cardinal thousand 8 and 60 =
millia-octo-sexagin-tillion)
357 * 10001068 (Latin power 1068 =
prefix cardinal thousand 7 and 60 =
millia-septen-sexagin-tillion)
In American system:
one hundred twenty three milliaduoseptuagintillion,
four hundred fifty six milliaunseptuagintillion,
seven hundred eighty nine milliaseptuagintillion,
two hundred forty six millianovemsexagintillion,
eight hundred one milliaoctosexagintillion,
three hundred fifty seven milliaseptensexagintillion
Compare the above name with the name we derived
back just before we reached Gigantic numbers.
When we added 3000 digits of 0's to the end of the number
(increasing the Latin power by 1000), we also added
millia as a prefix.
NOTE: To keep this web page from growing too large, we will
skip the full decimal listing of the numbers from now on.
Reaching larger numbers: the prefix rules continue as before.
When we add 3000 more 0's:
123 456 789 246 801 357 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
... 2000 sets of 000's omitted ...
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
We convert the above number into multiples of Latin powers as follows:
123 * 10002073 (Latin power 2073 =
prefix cardinal 2 thousand 2 and 70 =
duo-millia-duo-septuagin-tillion)
456 * 10002072 (Latin power 2072 =
prefix cardinal 2 thousand 1 and 70 =
duo-millia-un-septuagin-tillion)
789 * 10002071 (Latin power 2071 =
prefix cardinal 2 thousand 70 =
duo-millia-septuagin-tillion)
246 * 10002070 (Latin power 2070 =
prefix cardinal 2 thousand 9 and 60 =
duo-millia-novem-sexagin-tillion)
801 * 10002069 (Latin power 2069 =
prefix cardinal 2 thousand 8 and 60 =
duo-millia-octo-sexagin-tillion)
357 * 10002068 (Latin power 2068 =
prefix cardinal 2 thousand 7 and 60 =
duo-millia-septen-sexagin-tillion)
Thus, in the American system we have:
one hundred twenty three duomilliaduoseptuagintillion,
four hundred fifty six duomilliaunseptuagintillion,
seven hundred eighty nine duomilliaseptuagintillion,
two hundred forty six duomillianovemsexagintillion,
eight hundred one duomilliaoctosexagintillion,
three hundred fifty seven duomilliaseptensexagintillion
Here is an example with an additional 985 000 sets of 000's added:
123 456 789 246 801 357 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
... 987 000 sets of 000's omitted ...
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
We convert the above number into multiples of Latin powers as follows:
123 * 1000987073 (Latin power 987 073 =
prefix cardinal 900 7 and 80 thousand 2 and 70 =
nongen-septen-octogin-millia-duo-septuagin-tillion)
456 * 1000987072 (Latin power 987 072 =
prefix cardinal 900 7 and 80 thousand 1 and 70 =
nongen-septen-octogin-millia-un-septuagin-tillion)
789 * 1000987071 (Latin power 987 071 =
prefix cardinal 900 7 and 80 thousand 70 =
nongen-septen-octogin-millia-septuagin-tillion)
246 * 1000987070 (Latin power 987 070 =
prefix cardinal 900 7 and 80 thousand 9 and 60 =
nongen-septen-octogin-millia-novem-sexagin-tillion)
801 * 1000987069 (Latin power 987 069 =
prefix cardinal 900 7 and 80 thousand 8 and 60 =
nongen-septen-octogin-millia-octo-sexagin-tillion)
357 * 1000987068 (Latin power 987 068 =
prefix cardinal 900 7 and 80 thousand 7 and 60 =
nongen-septen-octogin-millia-septen-sexagin-tillion)
Thus, in the American system we have:
one hundred twenty three nongenseptenoctoginmilliaduoseptuagintillion,
four hundred fifty six nongenseptenoctoginmilliaunseptuagintillion,
seven hundred eighty nine nongenseptenoctoginmilliaseptuagintillion,
two hundred forty six nongenseptenoctoginmillianovemsexagintillion,
eight hundred one nongenseptenoctoginmilliaoctosexagintillion,
three hundred fifty seven nongenseptenoctoginmilliaseptensexagintillion
Astronomic size numbers ≥ 103000003
At the Latin power of 1000000 we have:
one nongen-novem-nonagin-millia-nongen-novem-nonagin-tillion
However at the Latin power of 1000001, we run out of prefixes!
It is at this point that we introduce our final rule:
the repeated prefix.
In the past, it was common to refer to million as "thousand thousand".
Thus a thousand millia becomes "millia millia".
And a million millia becomes "millia millia millia":
| Table 13 |
| Number |
Latin Power |
prefix cardinal |
prefix |
American system
with dashes |
| 103003 = 10001001 |
1001 |
1000 |
millia |
millia-tillion |
| 103000003 = 10001000001 |
1000001 |
1000000 |
millia millia |
millia-millia-tillion |
| 103000000003 = 10001000000001 |
1000000001 |
1000000000 |
millia millia millia |
millia-millia-millia-tillion |
| 103000000000003 = 10001000000000001 |
1000000000001 |
1000000000000 |
millia millia millia millia |
millia-millia-millia-millia-tillion |
| and so on ... |
und so weiter ... |
et ainsi de suite ... |
etcétera ... |
e assim por diante ... |
For example:
123 456 789 246 801 357 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
... 987 000 000 000 sets of 000's omitted ...
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
We convert the above number into multiples of Latin powers as follows:
123 * 1000987000000073 (Latin power 987 000 000 073 =
prefix cardinal 900 7 and 80 thousand thousand thousand 2 and 70 =
nongen-septen-octogin-millia-millia-millia-duo-septuagin-tillion)
456 * 1000987000000072 (Latin power 987 000 000 072 =
prefix cardinal 900 7 and 80 thousand thousand thousand 1 and 70 =
nongen-septen-octogin-millia-millia-millia-un-septuagin-tillion)
789 * 1000987000000071 (Latin power 987 000 000 071 =
prefix cardinal 900 7 and 80 thousand thousand thousand 70 =
nongen-septen-octogin-millia-millia-millia-septuagin-tillion)
246 * 1000987000000070 (Latin power 987 000 000 070 =
prefix cardinal 900 7 and 80 thousand thousand thousand 9 and 60 =
nongen-septen-octogin-millia-millia-millia-novem-sexagin-tillion)
801 * 1000987000000069 (Latin power 987 000 000 069 =
prefix cardinal 900 7 and 80 thousand thousand thousand 8 and 60 =
nongen-septen-octogin-millia-millia-millia-octo-sexagin-tillion)
357 * 1000987000000068 (Latin power 987 000 000 068 =
prefix cardinal 900 7 and 80 thousand thousand thousand 7 and 60 =
nongen-septen-octogin-millia-millia-millia-septen-sexagin-tillion)
which yields the following name in the American system:
one hundred twenty three nongenseptenoctoginmilliamilliamilliaduoseptuagintillion,
four hundred fifty six nongenseptenoctoginmilliamilliamilliaunseptuagintillion,
seven hundred eighty nine nongenseptenoctoginmilliamilliamilliaseptuagintillion,
two hundred forty six nongenseptenoctoginmilliamilliamillianovemsexagintillion,
eight hundred one nongenseptenoctoginmilliamilliamilliaoctosexagintillion,
three hundred fifty seven nongenseptenoctoginmilliamilliamilliaseptensexagintillion
See if you can verify the American names of the following
powers of ten:
| Table 14 |
| Example |
American system
with dashes |
| 103003 = 10001001 |
one millia-tillion |
| 1098025 = 100032675 |
one duo-trigin-millia-sescen-quattuor-septuagin-tillion |
| 103000003 = 10001000001 |
one millia-millia-tillion |
| 102570329536 = 1000856776512 |
one octingen-sex-quinquagin-millia-millia-septingen-sex-septuagin-millia-quingen-un-dec-illion |
| 103000000003 = 10001000000001 |
one millia-millia-millia-tillion |
| 101174743648579 = 1000391581216193 |
one trecen-un-nonagin-millia-millia-millia-quingen-un-octogin-millia-millia-duocen-sex-dec-
millia-cen-duo-nonagin-tillion |
| 103000000000003 = 10001000000000001 |
one millia-millia-millia-millia-tillion |
| 10696276510359811 = 1000232092170119937 |
one duocen-duo-trigin-millia-millia-millia-millia-duo-nonagin-millia-millia-millia-cen-septuagin-
millia-millia-cen-novem-dec-millia-nongen-sex-trigin-tillion |
So with this final rule, there is no limit to how high you can count!
European system
European system counting rules are similar to the American system.
They differ in one main aspect: The prefix cardinal is not one
less than the Latin power, it is half of the Latin power rounded
down to the next whole number.
Each prefix cardinal is used for 6 Latin powers.
When the Latin power is even, then we use a illion or
tillion ending.
When the Latin power is odd, then we use a illard or
tillard ending.
Latin powers in the American system go like this:
- thousand
- million
- billion
- trillion
- quadrillion
Latin powers in the European system go like this:
- thousand
- million
- milliard
- billion
- billiard
- trillion
- trilliard
- quadrillion
- quadrilliard
Traditional British system
Briefly, the Traditional British system long scale looks like the
European system in that the prefix cardinal is also
half of the Latin power rounded down to an integer.
However in stead of alternating between
illion or tillion ending and
illard or tillard ending,
we use a prefix of thousand for the odd Latin powers.
Latin powers in the Traditional British system go like this:
- thousand
- million
- thousand million
- billion
- thousand billion
- trillion
- thousand trillion
- quadrillion
- thousand quadrillion
Summary
To count in the American system and the Traditional British system
you need the following:
zero
one two three four five six seven eight nine
ten eleven twelve thirteen fourteen fifteen sixteen seventeen eighteen nineteen
twenty thirty forty fifty sixty seventy eighty ninety hundred thousand
mi bi tri quadri quinti sexti septi octi noni
un duo tre quattuor quin sex septen octo novem
dec vigin trigin quadragin quinquagin sexagin septuagin octogin nonagin
cen duocen trecen quadringen quingen sescen septingen octingen nongen
millia
See Table 2,
Table 5,
Table 6,
Table 11, and
Table 12.
With these endings:
illion or tillion
European system adds these endings:
illard or tillard
The Latin power always refers to a power of 1000.
In the American system the prefix cardinal is the Latin power minus one.
In the European system and Traditional British system the prefix
cardinal is half of the Latin power rounded down to the next whole number.
In the American system:
- The Latin powers ≤ 10 (prefix cardinal ≤ 9) are special cases.
See Table 2.
- When the Latin power, mod 100, is between 11 and 20 (prefix cardinal
is 10 thru 19), we use illion ending.
Note that this happens when the prefix ends in "dec".
- In all other cases we use the tillion ending.
In the European system and Traditional British system:
- The Latin powers ≤ 19 (prefix cardinal ≤ 9) are special cases.
- When the Latin power, mod 200, is between 20 and 39 (prefix cardinal
mod 100 is 10 thru 19), we alternate between the illion and
illard endings.
Note that this happens when the prefix ends in "dec".
- In all other cases we alternate between the
tillion and tillard endings.
When forming words from the prefix cardinal value, one must
say the units value before the tens value.
For prefix cardinals that are powers of 1000 > 1
(e.g, prefix cardinal of 1 000 000, 1 000 000 000, etc.)
we repeat millia.
We give a millia for each cardinal power of 1000.
With these rules, you can count as high as you want.
More examples
The following tables of the first 10000 powers of 10 may be illustrative:
Some of larger examples of the
English names of known
Mersenne Primes may also be useful examples.
Formal Latin vs. Informal Latin roots
This page was originally written using the informal latin system.
It has been changed to use formal latin system.
The English number system we use today is a mix of old English, old French
and old commercial Latin to name just a few sources. Extensions beyond
the Latin power of 21 was based in part commercial Latin of Venice,
particularly of the 14th and early 15th century when Republic of Venice.
This Latin differs from liturgical Latin and modern standard Latin
in several ways. One of these differences is "do" vs. "duo" as in
"do-dec-illion" vs. "duo-dec-illion", and is "du" vs. "duo" as in
"ducen-tillion" vs. "duo-cen-tillion". Additional differences include,
but are not limited to "millia" vs. "milia".
It is unfortunate that consistent spelling was not a hallmark of that era!
When we codifying the rules for "The English name of a number", we were
tempted to "improve" the system today. For example there are a number of
aspects to the system that we do not like. The inconsistency of "do/du"
(as in "do-dec-illion" and "ducen-tillion") and the "four and twenty"
rule (as in the name "quattuor-vigin-tillion") is unfortunate.
When we set down the "name of the number" system we were attempting
to programmatically describe the system we had using the roots of
the language on which it was based. If we tweaked the system to our
preferences in one place then soon we would have been describing our
preferences instead of the system we use today. So we resisted the
temptation to improve and stuck to strict codification of the names of
the Latin powers.
However since that time, we have uncovered use of "duo" in the 14th and
early 15th centuries. And since spelling then was often inconsistent (it
was not unusual to find a word spelled several ways in some documents),
we feel safe to select "duo" in the name of consistency. I.e., if we
are forced to choose a spelling, then we will opt for the more consistent
spelling that produces a simpler algorithm.
Regarding those proposing improved number naming systems
There exist a number of proposals offering improved number naming
systems. We agree that names of numbers used in English could be
improved if one was not interested in remaining backward compatible
with the system in use today. We also agree that the extension
beyond the Latin power of 21 may be improved if one is willing to
ignore the historic Latin power roots.
This page will NOT be modified to reflect such recommendations
for improvements for two important reasons:
- The "name of the number" system algorithm only describes an
extension to a historical system using the spelling and grammar
rules of that era. Modern Latin rules and more general proposals
for improved number naming systems are focused in ideas of
today, not what was in place centuries ago when the English
number naming system began.
- We do not have time or the energy required to codify alternate
proposals. While we wish the proponents of those systems success,
the purpose this algorithm is to describe the extension of the
common naming system today using the historic rules of th
languages on which today's system is based.
Regarding regional English language variations
There exist many of variations of the names of numbers in the English
language. Examples include this such as "zero" vs. "naught",
"thousand million" vs. "millard", "one thousand two hundred" vs.
"twelve hundred", "two hundred and forty" vs. "two hundred forty",
etc. English is a multifaceted language. English spelling and
grammar of New Zealand, Canada, Australia, U.K., U.S.A., just to
name a few places will differ. Even the output of digits can differ
among English speaking countries. For example: "123,456.789" vs.
"123 456.789".
This page just lists 3 of the many systems in the world.
Please accept our apology if we do not list your favorite.
A final historical note:
When I was 6, as part of the test to enter the 1st grade I was asked:
How high can you count?
A bit of background: Thanks to Chet, my brother,
at age 3 I know the prefix rules up thru decillion.
I had been attempting to memorize the numbers by
brute force, and had made it up to 117.
Chet came to my rescue by showing me the "trick" to counting.
With the help of a table from the Random House Dictionary
we had in our home, we learned the names of Latin powers up thru 11.
So with full confidence, at age 6, I answered:
nine hundred ninety nine decillion,
nine hundred ninety nine nonillion,
nine hundred ninety nine octillion,
nine hundred ninety nine septillion,
nine hundred ninety nine sextillion,
nine hundred ninety nine quintillion,
nine hundred ninety nine quadrillion,
nine hundred ninety nine trillion,
nine hundred ninety nine billion,
nine hundred ninety nine million,
nine hundred ninety nine thousand,
nine hundred ninety nine
The teacher was puzzled to say the least.
To be sure I had not made a mistake, I went to the board and
wrote out:
999,999,999,999,999,999,999,999,999,999,999,999
As I wrote it out, I named the groups "decillion, nonillion, ...".
I explained that if she told me the next name (for the Latin power
of 12, that is), I could add 3 more digits.
And so I waited for my "teacher" to supply me with
this word that would able me to count 3 orders of
magnitude higher.
For some reason I could not understand, my teacher sat in silence for
a while and then said:
"I don't believe you. Start counting."
I supposed I would have protested, counting was easy for me.
Counting fast was something I had practiced.
At age 6 I could count thru 100 in about 20 seconds.
After rounding 500 I began to wonder if she understood what
I was saying so I slowed down to show her I was really counting:
"... five hundred one,
five hundred two,
five hundred three ..."
and then switched back to my rapid counting pace.
As I was counting she said:
"Sit in the corner. I'll get back to your later."
So I sat down in the corner, not sure if I was being punished
or tested and continued counting.
I figured that I should count as high and as fast as I could
so I dropped my volume and went into high gear.
I used my left hand to keep track of the thousands digit
and my right hand to keep track of the hundreds digit.
(I had learned the trick of counting 1 to 10 on one
hand from my brother Chet.)
To save time I fully pronounced each multiple of a hundred
between rapid counts of 1 to 99.
When I rounded on 10000 I stick out my leg to record the
10000's digit.
Some 4 hours later (a huge span of time for a 6 year old) I
was rounding 21600.
I was beginning to get really tired and I had gradually slowed down
but I was still counting at a fast pace.
Well the teacher, who was testing other
students, noticed that I was still in the corner counting.
As she approached I slowed down and raised my volume so that
she could hear me better:
"... twenty one thousand, six hundred one,
twenty one thousand, six hundred two,
twenty one thousand, six hundred three, ..."
She then said:
"Oh, OK. You can stop now."
I was relieved because I had used by 2nd leg to mark 20000 and was
not sure what to do when I got to 30000.
She returned to my test paper and along side the question
"How high can you count?" she wrote:
over 100
I was mad.
I was more than mad, I was insulted!
I don't recall my reaction, but I'm sure it was not nice
as I was punished for whatever I did in response.
At this point I lost my trust in grammar school teachers.
I was sure that my teacher could not even say
the name of 1 000 000 000 000 000, so why
should I expect any teacher to know other facts?
In the years to follow I made it a point of
learning things on my own ... often at the expense
of not paying attention in class.
I'm sure I was a "difficult'" child in the classroom.
I'm not sure how things would have turned out if it were not for
a 7th/8th grade history teacher named Mr. Frank Tom
and 7th/8th science teacher named Mrs. Arbigast.
As you can see from
my bio,
I changed.
And to those teachers who helped: "Thanks!"
This page is dedicated to my good friend and brother,
Chet Leland Noll
who taught me the "trick" of counting when I was just 3
and introduced me to a lifetime of mathematics.
THANKS Chet!
Special thanks goes to Jeff Drummond for
answering my many questions about Latin.
|
