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1.2.5
Naming the numerals
A GUIDE ON HOW TO COUNT
Counting is such a basic yet essential skill, that kids learn it in early grade school. Any 5 year old should be able to count to 30. For this reason, this page should probably be considered more of reference material than anything else.
But for completeness sake I have included it, as section 1 "fundamentals of the counting numbers" covers the basics of labeling the smallest of the counting numbers, what I like to call the "counting range" which varies anywhere from 1 to a million or as high as ten billion (even though technically no one could really have a chance counting to ten billion ).
Let's get started then ...
THE 20 UNIQUE NAMES
Arguably, the names for the first 20 counting numbers are all unique. However, this is only partially true. The first 10 ten names are unique and not references to other numbers, but 11-20 are clearly derived through combining and altering other names.
The first 10 names are ...
Decimal Name
1 One
2 Two
3 Three
4 Four
5 Five
6 Six
7 Seven
8 Eight
9 Nine
10 Ten
The names don't seem particularly meaningful or logical in and of themselves. It's mainly through familiarity and repeatition that we come to strongly associate these words with part of a logical sequence. One odd thing is that their are pairs of adjacent names which start with the same letter. For example 2 and 3 begin with T , 4 and 5 with F, and 6 & 7 with S. No other pattern appears and the rest of the names seem to start with random letters ( although ten starts with t as well )
The next ten names are unusual ...
Decimal Name
11 Eleven
12 Twelve
13 Thirteen
14 Fourteen
15 Fifteen
16 Sixteen
17 Seventeen
18 Eighteen
19 Nineteen
20 Twenty
Perhaps the most notable feature is that 13-19 all end in -teen. Teen is likely a variation on ten. Notice that 14,16,17, and 19 amount to combining -teen with the appropriate number prefix.
For example by combining "four" and "teen" we get "fourteen". So "fourteen" literally means "four and ten" ( 4 + 10 ).
13,15, and 18 are the same idea except that the prefix is slightly altered as in ...
thir - teen
fif - teen
eigh - teen
a literal application of the construction would have lead to "threeteen", "fiveteen" and "eightteen". Obviously the double t was dropped for eighteen for good reason. Fifteen could be explained as a kind of contraction or verbal slur. dropping the "e" would lead to "fivteen", but v before t is harder to pronounce than f before t. Given the similiarities in the way the sound v and f are produced, f serves as a surogate sound.
As for thirteen, I can't think of a good explaination other than 2 sets of double e's looks repeative.
Eleven and Twelve are prehaps the oddest english number names. They don't seem to have much to do with the other names. Some probably wonder why they don't follow the teen pattern established through 13-19.
Apparently eleven and twelve are languistic relics of older numeration systems. Although it is often cited that humans use tenth base because we have ten fingers, many other numbers have been used as bases throughout human history including 5 , 20 , and even 60. Some even used base 12 systems. 12 might seem an odd number to choose as a base, except when you consider it's factors ( 1,2,3,4,6,12). It is a highly factorable, yet a relatively small number ( unlike 60 which is also highly factorable ). It is then ideal for divisions. Somehow the first 12 numbers have retained their uniqueness do to this influence.
However, if one looks carefully one can see, that they still roughly are related to the idea "one+ten" and "two+ten".
In greek one is sometimes transliterated as "enas", perhaps "elev" or "ele" is some kind of adaption for one. In that case eleven, might be understood as elev - (t)en .
With that in mind, it's tempting to consider whether twelve, has something to do with combing two with the root eleven, something like tw(o)elve.
Lastly twenty, meaning two groups of ten, could be understood as tw(o) - (t) en - ty .
COMBINING NAMING COMPONENTS
21~100
After 20, the names are no longer unique, but are rather combinations of naming components.
for example after twenty (20) , comes
twenty-one ( 21) , twenty-two ( 22) , twenty-three (23) , twenty-four (24) , etc.
Each name from 21~29 is formed simply by saying twenty, followed by the appropriate group of ones left over. Essentially your saying 20+1 , 20+2 , 20+3 , etc.
To continue past 29 properly, you need to know the names for the groups of tens.
The chart below shows them ...
Decimal Groups of Ten Name Component Possible derivation
30 3 of ten Thirty thir(=three) - ty*
40 4 of ten Forty fo(u)r - ty
50 5 of ten Fifty fif(=five) - ty
60 6 of ten Sixty six - ty
70 7 of ten Seventy seven - ty
80 8 of ten Eighty eigh(t) - ty
90 9 of ten Ninety nine - ty
* ty might be a contraction of ten. ten --> te --> ty . In this case seven-ty might be understood as "seven times ten".
Using the words for 1~9 and the naming components for groups of tens, it is now possible to name numerals up to 99.
To name any 2-digit number, simply say the group of ten component corresponding to the first digit followed directly by the group of ones component corresponding to the second digit.
Ex.
38 --> thirty-eight
62 --> sixty-two
When there is zero in the ones position, simply say the group of ten name alone ...
70 --> seventy
So what comes after 99 ? 100 is given a unique name component, "hundred".
100 could be read as " a hundred" or " one hundred", but not just as "hundred". If your not convinced just consider this sentence ...
" I own a hundred cats "*
you could also say " I own one hundred cats exactly "
but it sounds awkward to say " I own hundred cats"
Oddly we don't add indefinite articles to other numbers. For example you would say " I own three cats" but not " I own a three cats "
The use of the article "a" suggests that "hundred cats" is being treated collectively as a single object.
*Note: just for the record, I don't own a hundred cats, it's just an example sentence.
THE FIRST NAMING BLOCK
1~999
We already have all the naming components neccessary to name all the numerals up to 999.
To name a 3 digit number, you first specify the first digit with the usual labels ( 1 = one , 2 = two etc. ) followed by the word "hundred". Next say "and" followed by the appropriate group of ten component and lastly the group of ones component.
For example ...
583
five hundred and eighty three
This is originally the way I learned to say them in grade school. I remember I was pretty veminant that that was the proper way to say them.
However, it is common to contract the "numeral name" by dropping the "and". In fact one can even get away with dropping the "hundred" as well. In this case it would be acceptable to say five eighty three, and still be understood most of the time ( although in the US if you tell someone something costs five eighty three, it might mean 5.83 USD instead of 583.00 USD )
I've actually come to like this truncated version because of its compactness.
When there is a zero digit, just drop the appropriate component, so for example 304 would simply be three hundred and four. Note however that if we drop "hundred and" we will get an ambigious "three four". In this case one can insert "oh" as the sound for the zero, thus you will often hear things like "three oh four"
Using these conventions we can name all the numerals up to 999 which we can call "nine ninety nine".
What would we call 1000 then? Would "Ten hundred" be acceptable? You could use that, but it is more common to say "a thousand" or "one thousand".
Learning to count to a thousand is sufficient for most ordinary tasks. It also may occur to you that based on the naming pattern one could continue with things like "a thousand and one" (1001) , " a thousand and two" (1002) , etc. and you'd be right.
After a thousand, naming falls into a regular pattern, which breaks up the name into blocks of 3 digits.
The 2nd Block and Beyond
1001~ ????
When their is no units in the hundred position you can insert an "and" or "oh" between thousand and the following naming components.
For example 1003 would be "one thousand and three". You wouldn't use oh in cases where there is also no tens units though.
In cases such as 1069 you can say either "one thousand and sixty nine" or "one thousand oh sixty nine".
When their are hundreds units the "and" is dropped. for example 1234 would be "one thousand two hundred and thirty four"
Now we need to discuss blocks. Recall in the last article that decimals are sometimes seperated with commas. Specifically a comma must be inserted every 3 digits.
So a numeral like 4532 would be written 4,532. The comma is seperating the first block ( units block ) from the second block ( thousands block )
Likewise the word "thousand" is seperating the first and second block within the numeral name.
It is possible to name all the numerals up to 999,999 using only the components we have already specified.
Basically the form is " X thousand Y " where X is the number of thousands specified in the 2nd block, and Y is the number of units in the first.
For example something like 32,768 would be ...
" thirty two thousand seven hundred and sixty eight "
It this way we can even have hundreds of thousands, for example ...
262,144 is "two hundred sixty two thousand one hundred fourty four"
So that means that 999,999 would be ...
"nine hundred ninety nine thousand nine hundred ninety nine "
So how does one proceed then ... ? what would 1,000,000 be ?
That is the beginning of the third block (which comes after the first two commas ).
Each block has a seperating word, and each block itself is formed by the groups of 3 digits as XYZ is "X hundred and (Y)-ty Z".
The next block word after "thousand" is "million" which means "great thousand". Most people have heard of a million before.
One then continues by specifying the number of millions followed by the number of thousands followed by the number of units.
For example 12,456,789 would be
"twelve million four hundred fifty six thousand seven hundred eighty nine"
You can already see that the "names" are becoming quite long. It should be pretty clear how to name all the numerals up to 999,999,999 at this point.
The key to continuing is to know as many "block denominations" as you need and/or want.
The chart below shows the most commonly known and used block denominations ...
DECIMAL START OF ... NAME COMPONENT
1,000 2nd block thousand
1,000,000 3rd block million
1,000,000,000 4th block billion
1,000,000,000,000 5th block trillion
1,000,000,000,000 6th block quadrillion
1,000,000,000,000,000 7th block quintillion
Most people know about millions, billions, and trillions, but many people are unsure what comes after that. Part of this has to do with the fact that magnitudes greater than a trillion are rare except in science. Scientists rarely use words like quadrillion and quintillion and instead make use of scientific notation, and often even popular science magazines will use things like million billion, and billion billion, because quadrillion and quintillion are not widely known.
For these reasons these naming components are regarded more as trivia. You might object however, and state that it is simply a matter of completing the counting system. The problem with that idea is where should one choose to stop counting ? Clearly we can not name all counting numbers, and at some point we must stop.
In any case, this is more than sufficient for basic counting because a human couldn't count higher than a billion even if they counted for their entire lives !
Keep in mind that in the sequence thousand , million , billion , trillion , etc. each new term is one thousand times greater than the last ! As we will see later these terms have been extended well beyond quintillion , to the point of absurdity. Eventually however, even these extensions break down. But these are topics we will look more into in section II : The -illion series.
For now be content with counting to 999,999,999,999,999,999,999 which is ...
" nine ninety nine quintillion nine ninety nine quadrillion nine ninety nine trillion nine ninety nine billion nine ninety nine million nine ninety nine thousand nine ninety nine "
In the next article is a chart that shows how numerals are named in many different languages around the world and throughout history ...
Next article: 1.2.5 - Counting in 14 Different Languages
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