David's SI metric FAQ

Updated 2002-07-09. Please send me relevant links. Contents:

related pages:

The metric system = the SI standard = ISO 31-0:1992

SI Metric Prefixes (Système International)

I get the impression that not everyone here has a handy metric prefix chart. I use it often (but then, I use mA (milliAmpere), pF (picoFarad), and MHz (MegaHertz) every day).

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 SI Metric Prefixes

 power of 1000
 			power of 10
 				nearest power of 2

  8	Y	yotta	24	80
  7	Z	zetta	21	70
  6	E	exa	18	60
  5	P	peta	15	50
  4	T	tera	12	40
  3	G	giga	9	30
  2	M	mega	6	20
  1	K *	kilo	3	10
  0			0	0
 -1	m	milli	-3	-10
 -2	u *	micro	-6	-20
 -3	n	nano	-9	-30
 -4	p	pico	-12	-40
 -5	f	femto	-15	-50
 -6	a	atto	-18	-60
 -7	z	zepto	-21	-70
 -8	y	yocto	-24	-80

[*] The official prefix for micro is µ. If the Greek small letter mu μ is unavailable, use the Roman letter "u". Do not use "m".

Official reference: NIST metric page and ISO, the International Organization for Standardization http://www.iso.org/ (was http://www.iso.ch/ )

Often we want to refer to some exact power-of-2 units and sizes.

According to http://physics.nist.gov/cuu/Units/binary.html , when things naturally come in powers-of-2, one can tack a "i" to the prefix above to indicate an exact power-of-1024 (rather than the above exact power-of-1000). So now we have b (bits), Kib (kibibits = 2^10 bits), Mib, Gib, Tib, Pib, Eib, Zib, Yib (yobibits = 2^80 bits). I (David Cary) be interested in hearing if anyone ever used this sort of notation for numbers less than one. (For example, some pictures can be compressed to an average of 0.88 bits/pixel; would this be 880 mibibits ?)

The http://www.ibiblio.org/mdw/HOWTO/Large-Disk-HOWTO-3.html#s3 and http://www.wins.uva.nl/~mes/jargon/q/quantifiers.html also talk about using metrix prefixes to deal with exact-powers-of-2.

Unofficial reference:

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[*] Why did some standards organizations use lowercase k for kilo, rather than Uppercase K ? Other people http://physics.nist.gov/cuu/Units/binary.html also recognize that Uppercase K gives the best consistency. If we capitalize K for kilo, then we have a simple and consistent capitalization rule:

Prefixes that make things BIGGER (positive exponent) are a Capital Letter. Prefixes that make things smaller (negative exponent) are a lowercase letter.

The unit itself is capitalized if it is named after a person ( A Ampere, V Voltaire, etc.) but lowercase otherwise (m meter, s second).

This is critically important for the prefixes "M" vs. "m", "Y" vs. "y", "Z" vs. "z".

For example: ``one inch is exactly 25.4 mm''. ``The surface of Sol, Earth's sun, has a temperature of about 5.8 KK, with occasional 3.8 KK sunspots.''.

More random factoids about the SI system of units.

The SI standard way of saying "10^9 species" is "1 G species" (I think). I don't understand why anyone would use that ambiguous term "billion", since it means something completely different in the British English than it does in the American English, and it doesn't mean anything at all in all other languages, while Giga is the international standard and means the same thing in French, English (all kinds), Russian, etc.

The circumference of Earth is almost exactly 40 Mm (because the French originally defined the meter to be 1/(10 000 000) of the surface distance between the equator and the N pole).

The speed of light in free space is *defined* to be (approximately) 300 Mm/s. In more convenient units, that's 0.3 m / ns (about 1 foot per nanosecond). (see NIST for the exact number)

Here are the oddball SI prefixes. Maybe if I leave them off the main chart they'll go away and stop bothering me.

power of 10

2	h	hecto
1	da	deka
-1	d	deci
-2	c	centi

Sources of info

Van Isaac Anderson is putting together a page of obsolete and rare metric prefixes http://www.cs.uidaho.edu/~ande5754/prefix.htm .

Van Isaac Anderson has been searching for the abbreviation 10^-4 "for a long time with no success." On the other hand, he has found 10^+4 "my" "myriad"; "You can look it up in American Heritage Dictionary (under metric system, it gives a few examples, myriameter, myriagram, myriare, & myrialiter), in a good Webster's (under myria), or in the Merck index, 12th edition: miscelaneous tables: Universal Conversion Factors: myriagrams, myriameters, myriawatts. This is on page MISC 74." ...

"It is derived from the word "myriad", which used to mean 10 thousand, but now tends to just mean "many"." ...

"the abreviation is "my-", following the lead of hecto- "h-", deka- "da-", and kilo- "k-", in not generally being capitalized. This is probably based on the fact that "My" could mean Mega-years" ...

"I feel that it is a part of our metric cultural heritage, and deserves to be recognized, as it is largely forgotten, even in the internet metric community." "For a more comprehensive look at metric time, you may want to go to altavista and do the following search: "metric+time - sci.anthropology", sans quotes."

Van Isaac Anderson http://www.geocities.com/SiliconValley/Pines/8250/mtime.htm

DAV: my dictionary, _Webster's Seventh New Collegiate Dictionary_ (c) 1971 by G. & C. Merriam Co. Under "myriad" one definition is 10 000. It lists a "myriameter" which says "see METRIC SYSTEM table". In turn, that table lists the "myriameter (mym) = 10,000 meters" which is the only mention of myria- (my-); the only mention of 10^-4 is "square centimeter = sq cm = cm^2 = 0.0001 square meters"

Markus Kuhn (Date: 17 Oct 1995) says

If you are interested in having a copy of ISO 1000 (a.k.a. the metric system), I highly recommend the book

Quantities and units,
ISO Standards Handbook,
International Organization for Standardization,
345 pages, 3rd edition, Geneva, 1993,
ISBN 92-67-10185-4.

For ordering information, check http://www.iso.ch/ or mail to sales@isocs.iso.ch. I guess, every good bookshop will also be able to order it, as is your national standards body (ANSI, DIN, AFNOR, etc.).

Markus Kuhn (Date: 17 Oct 1995) asks

There is some work going on on replacing the definition of the kilogram by one which does not depend on a prototype. Does anyone know the status of this?

From:  Markus Kuhn
Newsgroups: ...,comp.misc,...,eunet.europen,...
Subject: Re: Programming Contest
Date: Mon, 17 Oct 1994 19:20:41 GMT
Organization: Student Pool, CSD, University of Erlangen, Germany
>Didn't the SI standard (the one that defines the various metric units) not
>specify that a dot be used for decimal separation, and a space for thousands ?

Yes. The official text of the SI standard (ISO 31-0:1992) is:

3.3.2  Decimal sign

The decimal sign is a comma on the line.
If the magnitude is less than unity, the
decimal sign should be preceded by a zero.

NOTE 17  In documents in the English language, a dot is
often used instead of a comma. If a dot is used, it should
be on the line. In accordance with an ISO Council decision,
the decimal sign is a comma in ISO documents.
Markus Kuhn, Computer Science student -- University of Erlangen,
 - Germany
WWW Home: <http://wwwcip.informatik.uni-erlangen.de/user/mskuhn>


Links to Standards Organizations:


see also computer_graphics_tools.html#txt for more about text files (.txt).

[FIXME: A lot of this stuff is now obsolete. Delete the bad stuff, hold on to the good. ] [FIXME: Consider switching from ISO 8859-1 to ISO 8859-15. Is the euro symbol the only difference ? € &euro; ]

related local pages:


index --> si --> ISO --> ambiguity

things I don't like about ISO-8859-1

Incorrect letters DAV commonly encounters:

Those incorrect letters aren't really the fault of ISO-8859-1. They're the fault of someone using some non-standard ``charset'' and then neglecting to tell us which charset that person used.

Far too many web pages have an incorrect ``charset'' specified, then use decimal ``Numeric reference''. (I suspect that most of the time the HTML editor is to blame, not the web page author -- it looks fine on his machine ...). This causes decimal references between &#127 and &#255 inclusive (since they are different between Macintosh and Windows, and vary even between different versions of Windows), to display completely different symbols on different machines.


Some real flaws I see in this character set ISO-8859-1: it is missing a few common characters (well, they're common in DAV's writing):

I wish the original ASCII standard had included both left and right quotes. The "unterminated string error" which happens all too frequently (and gives terribly misleading error messages on every compiler I know) would have been so much easier to catch and correct.

( The "ASCII Character Code Reference" by Frank Durda IV 1975, 2008 http://nemesis.lonestar.org/reference/telecom/codes/ascii.html mentions "numerous symbols that do not exist in ASCII but might seem logical to have." )

2002-07-25:DAV: All these entities display properly in HTML 4.0 compliant web browsers for some time now (I first noticed this 2001-12-02 ) (even the &trade; "™", which hasn't really been officially opproved yet). . .

There are several ways to work around these missing characters:


things I do like about ISO-8859-1

When I originally wrote this page (back in 1995), The default character set for pages on the web was the ISO-8859-1 character set.

Now it seems everyone's moving to Unicode , making this section more and more obsolete.

( "HTML uses the much more complete character set called the Universal Character Set (UCS), defined in [ISO10646]. This standard defines a repertoire of thousands of characters used by communities all over the world. The character set defined in [ISO10646] is character-by-character equivalent to Unicode 2.0 ([UNICODE]) http://www.unicode.org/ ." -- http://www.w3.org/TR/REC-html40/charset.html )

Still, the subset of Unicode known as ISO-8859-1 still has some features I like.

I still think the ISO-8859-1 is pretty useful. All the text I write can be represented in it (and of course in Unicode, since ISO-8859-1 is a subset of Unicode). (OK, so I cheat a little doing entity codings for Greek letters, while Unicode can represent them directly). When I can do something 2 different ways, one way that can be described on a T shirt, while the other way requires a weighty book, I much prefer the T shirt. simplicity . local.html#t-shirt

ISO-8859-1 is built into the HP48 calculators. I doubt that Unicode would fit in the tiny ROM available on such devices. (the HP48 also has a few extra symbols ... pi, delta for derivatives, integral symbol, up down left right arrows, theta, alpha, Omega the Ohms symbol, ``lazy-8'' infinity). hardware_david_uses.html#hp48

This set easily handles the standard Deutsch character set, including

Ä &Auml; Ë &Euml; Ï &Iuml; Ö &Ouml; Ü &Uuml; ; ß &szlig; ; ä &auml; ë &euml; ï &iuml; ö &ouml; ü &uuml; .

Also Español: Ñ &Ntilde; ñ &ntilde; .

You can easily view the full ISO-8859-1 character set at once. That's not possible with Unicode.

A single typographer can feel confident that he's producted a "complete" ISO-8859 font. I doubt there's any single person that can produce a "complete" Unicode font.

You may want to look at a picture of the full ISO-8859-1 character set ftp://swrinde.nde.swri.edu/pub/png/documents/iso_8859-1.png mirror ftp://ftp.uu.net/graphics/png/documents/iso_8859-1.gif or alternatively pictures of what the various ISO-8859-n character codes are *supposed* to look like. Then you can look at what your browser actually displays for those codes #entities .

While there are many pretty typographic symbols that have been left out of ASCII, it has been proven that all possible typographic symbols can be encoded by sequences of ASCII symbols. See to_program.html#pretty_print for one particular way of using plain ASCII to indicate italics, bold, etc.

http://www.robotwisdom.com/net/etextfaq.html seems to agree that Unicode is too complicated .... is in favor of plain 7-bit US-ASCII, 80 columns wide.


other random information about ISO-8859-1

You may also be intereted to know the standard color names and what your browser actually displays for those color codes. .

DAV understands that the particular shape of a character has no meaning itself. A particular letter means the same thing to me, even if it looks very different in different fonts. In particular, the letters 'g', 'q', and the vertical bar often look very different in different fonts.

See also:

[FIXME: --------------------------------]

µ (micro)

The word ``micro'' comes from the Greek word ``μικρος'', meaning ``small''.

Since modern technology (Moore's law) has been so intensely focused on making things smaller and smaller, many people abbreviate that word to just the first letter in the Greek word, μ, the Greek letter mu, and call it the micro sign.

For example, the µprocessor (pronounced ``micro-processor''), µcomputer, µswitch, etc.

The micro sign is just as much a character in the ISO-8859-1 character set set as the Roman letter "a". A correctly-functioning browser will display 4 micro signs here: " ´ µ µ µ ".

W3C in their list of character entities http://www.w3.org/TR/html4/sgml/entities.html#h-24.3 lists these 2 distinct entites:

I confess I can't tell the difference. Is there a real difference between them ? Other Greek letters.

π (pi)

Unfortunately, using the Greek letter pi is more difficult.

Here are the methods I know to render the Greek letter pi on a web browser, although none of them are really satisfying:
"¹" and "¹" or "¼" and "¼" sometimes works with Macintosh browsers
"p" often works with Mac and Windows browsers
"pi" works with any graphical browser, but doesn't give the appropriate height for the text.

Unfortunately, some browsers will display one correctly, others will display a different one correctly. There seems to be no single "best" method for someone like myself to make sure you see a pi character. I wish for a standard "&pi;" character entity.

Late breaking news: W3C has made π (&pi;) easy to use.

Alan Flavell has work-arounds and recommendations on the (TM) symbol, as well as lots of other useful information on ISO-8859.

More official information on the HTML character set http://www.w3.org/TR/PR-html40/charset.html

More symbols from http://www.w3.org/TR/html401/sgml/entities.html#h-24.3 /* was http://www.w3.org/TR/REC-html40/sgml/entities.html#h-24.3 */ :

"™" &trade; Trademark symbol
"ℵ" &alefsym; alef symbol = first transfinite cardinal
"·" &middot; middle dot = Georgian comma = Greek middle dot

"←" leftwards arrow
"↑" upwards arrow
"→" rightwards arrow
"↓" downwards arrow
"↔" left right arrow
"↵" downwards arrow with corner leftwards = carriage return
"⇐" leftwards double arrow; can be used for 'is implied by'
"⇑" upwards double arrow
"⇒" rightwards double arrow; can be used for 'implies'
"⇓" downwards double arrow
"⇔" left right double arrow; DAV: thinks this can be used for "if and only if".
"Ø" latin capital letter O with stroke (sometimes used to indicate zero, to emphasize it is different from the character Oh).
"°" degree sign (note that it is incorrect to use this with Kelvin; the boiling point of nitrogen is about 60 K (pronounced "60 Kelvin"), *not* "60 °K" or "60 degrees Kelvin").

http://www.ngs.fi/mtr/genscript/ points to a nice ISO-8859-1 chart, listing hex code, printable character (if any), Postscript code, HTML entity (if any).

[FIXME: Think about describing my *own* character set. Most of my documents are labeled as <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> but actually use a few extra letters via the ampersand escape mechanism ... I think (?) that all those extra letters are easily represented in iso-8859-1. List all the characters I use. ]

Programming for Internationalization FAQ http://www.vlsivie.tuwien.ac.at/mike/i18n.html comp.std.internat

"English", "Imperial", "Standard", "American" units

Apparently the "Imperial" units were based on the binary system.

From:  Robert A. Uhl
Newsgroups: alt.folklore.science,...,sci.history,sci.physics
Subject: Re: Metric Time (was Re: Why not 13 months? (Was La Systeme Metrique))
Date: 17 Oct 1995 15:35:25 GMT
  Sometime last century our government replaced the old sensible
system os two mouthfuls = 1 jigger, 2 jiggers = 1 jack, 2 jacks = 1
jill (or gill), 2 jills = 1 cup &c. with 8 fluid oz. = 1 cup.  So a
fl. oz. is a jigger.

  Jiggers are still used, esp. when pouring drinks.  And cups must be
marked 1/2 cup because few remember what a jill is.  Silly.  But the
enthusiasts who actually care know.  SIgh.

| Bob Uhl | Spectre                  | `En touto nika' +                 |
| U of D  | PGG FR No. 42            | http://mercury.cair.du.edu/~ruhl/ |

And 2 cups = 1 pint, 2 pints = 1 quart, 2 quarts = 1 pottle, 2 pottles = 1 gallon, 2 gallons = 1 peck, 2 pecks = ???; 2 ??? = 1 bushel, 2 bushels = 1 strike or cask; 2 casks = 1 barrel (32 gallons), 2 barrels = 1 hogshead, 2 hogsheads = 1 pipe, 2 pipes = 1 tun (a tun of water weighs 2 120 pounds). -- http://www.xtronics.com/jackandjill.htm http://wiki.xtronics.com/index.php/Jack_and_Jill


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