## How high can you count?

[chongo's home] [Astronomy] [Mathematics] [Prime Numbers] [Programming] [Technology] [contacting Landon]

# 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:

1. thousand
2. million
3. billion
4. trillion
5. quadrillion

Latin powers in the European system go like this:

1. thousand
2. million
3. milliard
4. billion
5. billiard
6. trillion
7. trilliard
8. quadrillion
9. 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:

1. thousand
2. million
3. thousand million
4. billion
5. thousand billion
6. trillion
7. thousand trillion
8. quadrillion
9. 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:

1. 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.

2. 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.

 © 1994-2013 Landon Curt Noll chongo (was here) /\oo/\ \$Revision: 7.9 \$ \$Date: 2015/09/30 02:00:29 \$