CONstant conSTRUCTION - Forward into the Unknown... All original material © William J. Park, Jr.
Numbers
(That which makes one numb?)

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| Metric Prefixes | Named Numbers | Roman Numerals |

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SI (Metric) Prefixes

The current system of units adopted throughout the entire civilized world (except those irrational weirdos, the citizens of the United States of America) was originally formulated by the French (thus SI which is an abbreviation for Le Système International d'Unités) and is now commonly called the Metric System.

The standard prefixes used with the Metric System allow us to conveniently and compactly express both very large and very small quantities by representing powers of ten. Except for powers with magnitude less than 3 (10^-2, 10^-1, 10¹, and 10²) the prefixes correspond to powers of ten which are multiples of 3 (10³, 10^-9, etc.) (In the table below, the prefixes corresponding to powers of ten which are not multiples of 3 are shown in red. These are used less frequently in engineering with the exception of centi-: the centimeter is a very commonly used unit of length.)

The metric prefixes are meant to be used with units (e.g. milli-meters or kilo-grams) not with unitless numbers.

Until recently, the standard prefixes only extended to 10¹⁸ and 10^-18. As science has marched farther into the huge (the cosmos) and the tiny (quarks) it has become more common to need extremely large and small numbers so two new prefixes were invented on each end of the scale.

Note that the abbreviations for positive powers of ten are usually capitalized and those for negative powers of ten are usually in lower case. This prevents confusion between terms like Peta- and pico, or Mega- and milli-.

In order to talk about numbers (as opposed to writing about them), we need names for them. I will assume everyone reading this is familiar with the smaller numbers' names, like seven, twelve, thousand, and million, as well as combinations like twenty-three or two hundred seventy-five million forty six thousand one hundred and eighty four.

Above 999,999,999 (which I'll be durned if I'm going to write out) things get a bit strange. First of all, there are two primary naming systems in English, the American and the British. In my opinion, the American nomenclature stomps all over the British since it derives directly from the number of zeros in the number. Also, since I live in the good old US of A, I am familiar with this system, as are most of my students.

If the number of zeroes are grouped into threes (often indicated by commas when writing a number using numerals - e.g. 1,000,000) the prefix in front of "-illion" derives directly from the Latin terms for the number of groups of three zeroes. Unfortunately, it has an offset of one group of three. Example: Billion has the prefix bi- meaning 2. The number one billion (remember, this is the American system, the British is different) is 1,000,000,000. Note that there are 2 groups of three zeroes following 1,000. Trillion (tri- means 3) is 1,000,000,000,000. Tillion has 3 groups of three after 1,000.

The following table lists all named numbers (or rather names of numbers equal to 10 raised to an integer power which is a multiple of three) up to 20 groups of three zeroes following 1,000, plus the number with 100 such groups. Anyone familiar with Latin can easily determine the names of all the numbers in between vigintillion and centillion. (By the way, in Latin, "v" sounds like the English "w", and the "g" is always "hard" as in "go".)

In addition, there are a couple of other named large numbers that do not fit this pattern. First is the Googol, which is a 1 followed by 100 zeros (10¹⁰⁰). To put this sort of number in perspective, the most recent estimate (about 1996) I have seen for the number of sub-atomic particles in the known universe ( in all the billions of galaxies, etc.) is about 10⁸⁰! A googol is VERY big.

Now, if you want to be totally ridiculous, there is the googolplex, which is a 1 followed by a googol zeroes, in other words
One googolplex = 10^googol or
10 ^{10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} !!!
GOOD GRIEF!

I do not intend to write a treatise on composing numbers using Roman Numerals, since their use is limited to a few specialized contexts, e.g. dates in certain contexts (copyright dates of movies for instance), page numbers in prefaces to books, etc. If you really care about how to write 3,799,024 in Roman Numerals and don't know the rules, you will have to seek elsewhere. If you know the construction rules, the following will allow you to construct most reasonable sized (whatever that means) numbers using Roman Numerals. Roman Numerals may be written in either upper or lower case letters, but should not use mixed case in one number.

Number	Roman Numeral
1	I
5	V
10	X
50	L
100	C
500	D
1,000	M
5,000
10,000
50,000
100,000
500,000
1,000,000