Measurements and Units
(Calvin of Farina, IL.
2000-11-05)
Current and Deprecated Prefixes
What are all of the metric prefixes?
Official SI metric prefixes (largest to smallest)
and deprecated metric prefixes (obsolete or bogus)
| SI | Value | Remarks |
Obsolete |
Bogus |
| |
1033 | |
una, vendeka (V) |
| 1030 | |
dea, weka (W) |
| 1027 | |
nea, xenna (X) |
| yotta- | Y |
1024 | Adopted in 1991. |
otta |
| zetta- | Z |
1021 | Adopted in 1991. |
hepa |
| exa- | E | 1018 |
Adopted in 1975. |
| peta- | P | 1015 |
Adopted in 1975. |
| tera- | T | 1012 |
Adopted in 1960. | megamega (MM) |
| giga- | G | 109 |
Adopted in 1960. | kilomega (kM) |
| mega- | M | 1000 000 |
CGS system since 1874. Legal in France since 1919. |
| | 100 000 |
| hectokilo (hk) |
| 10 000 | | myria (ma, my) 1795 |
| kilo- | k | 1000 |
Since 1793. |
| hecto- | h | 100 |
Since 1793. |
| deca- | da | 10 |
Since 1793. Also deka. | dk |
| | | 1 |
Unprefixed. |
| deci- | d | 1/10 |
Since 1793. |
| centi- | c | 1/100 |
Since 1793. |
| milli- | m | 1/1000 |
Since 1793. |
| |
1/10 000 | | decimilli,
dimi (dm) | myrio (mo) |
| 1/100 000 | | centimilli (cm) |
| micro- | m,u | 1/1000 000 |
Within CGS system since 1874 (BAAS). |
| nano- | n | 10-9 |
Adopted in 1960. | millimicro (mm) |
| pico- | p | 10-12 |
Adopted in 1960. | micromicro (mm) |
| femto- | f | 10-15 |
Adopted in 1964. |
| atto- | a | 10-18 |
Adopted in 1964. |
| zepto- | z |
10-21 | Adopted in 1991. |
ento |
| yocto- | y | 10-24 |
Adopted in 1991. |
fito |
| | 10-27 |
|
syto, xenno (x) |
| 10-30 | |
tredo, weko (w) |
| 10-33 | |
revo, vendeko (v) |
The use of metric prefixes dates back to the inception of the French metric system, in 1793.
It was originally decided that the submultiples of all basic units would be prefixed
with a Latin root, corresponding to the decimal divisor
(deci for 10, centi for 100, milli for 1000), whereas the decimal
multiples would be prefixed with a Greek root, corresponding to the decimal
multiplier (deca for 10, hecto for 100, kilo for 1000).
In 1795, the Greek root myria for 10000 was added to the latter list
(it's now officially obsolete, see below).
There was soon an obvious need to extend the system beyond its original limited range.
The prefix micro (from the Greek mikros, small) was introduced to denote
one millionth of the basic unit. The prefix mega
(from the Greek megas, great) appeared around 1870
to denote a million times the basic unit.
It used to be acceptable to combine two prefixes (see above "obsolete" column).
In 1960 however, it was decided to name only powers of 1000,
not intermediary powers of 10, except for the original 1793 prefixes
(the popular myria prefix was thus deprecated in the process).
Four additional prefixes were introduced at that time:
pico (Spanish pico beak, small quantity),
nano (Greek nanos, little old man, dwarf),
giga (Greek gigas, giant),
tera (Greek teras, monster).
It was then decided that the names of future prefixes should serve as reminders of
the relevant power of 10.
This started in 1964, with the introduction of femto and atto
(Danish or Norwegian: femten for 15, atten for 18).
The former prefix was particularly convenient, because it made the widespread
abbreviation fm (for "fermi") correspond correctly to the
the officially endorsed femtometer.
After that, however, it became clear (!?) that since only powers of 1000
were to be named, the prefixes should reflect the ranks of the powers of 1000 involved.
This is why, in 1975, the prefix exa (Greek hex, 6) was chosen for
1018=10006,
whereas peta (Greek pente, 5) was picked to represent
1015=10005.
The four latest prefixes, which were made official in 1991, are also supposed to remind
an international audience of the relevant powers of 1000:
yocto (1000-8),
zepto (1000-7),
zetta (10007), and
yotta (10008);
the trend being that the ending "a" is used for large powers,
while "o" is used for small ones.
The 5 exceptions to this modern rule are all the 1793 prefixes, except deca
(for these 6 "low" prefixes,
the long forgotten Greek/Latin distinction applies, as mentioned above).
The last column of the above table lists as bogus 10 extreme prefixes
(revo, tredo, syto, fito, ento, hepa, otta, nea, dea, una).
The larger of these follow the etymological pattern described above,
and 4 of them "compete" with the latest official SI prefixes.
These bogus prefixes have apparently not been used by anyone and
are not endorsed by anybody, but they show up
in tables which have been floating around in Cyberspace...
This is probably the result of a minor hoax perpetrated sometime
around 1996.
[2003-06-22 update:]
Other dubious prefixes are also shown
(vendeka, xenna, xenno, vendeko)
which we discuss elsewhere.
Please, tell us
whatever you know about the issue...
Note (2002-05-01) :
Usenet
Archives show
Alejandro López-Ortiz
posting 3 times, between 1998 and 2000,
a bogus list of prefixes ["7.5" dated 1998-02-20]
whose previous version ["7.1", dated 1995-12-31, last posted 1996-10-09]
didn't include any bogus information...
In a 2002-01-14 post,
Robi Buecheler plagiarized the above
text...
On 2004-12-14, Robi Buecheler
apologized:[...]
I should have given you credit [and/or posted a] link.
Sorry. |
Bogus prefixes are not spreading out of control.
However, at least one (careless) science-fiction writer has been fooled:
In his 2003 novel entitled Schild's Ladder, Greg Egan uses
the two bogus prefixes xenno and vendeka as if they
were legitimate.
(Thanks to Tom Alcorn for pointing that out, 2007-12-05.)
(J. B. of New Lenox, IL.
2001-02-09)
How many kilobytes [kB or "K"] in 2 "megs" [megabytes, MB]?
For units of information that are multiples of the bit (and only these),
the multiplicative prefixes kilo- mega- giga- tera- etc. do not have their usual
meaning as powers of 1000.
They are powers of 1024 (2 to the power of 10) instead.
Thus, a kilobyte (kB) is 1024 bytes and a megabyte (MB) is 1024 times that
(namely 1048576 bytes). Therefore, 2 "megs" is 2048 kilobytes.
A gigabyte (GB) is 1024 MB (1073741824 bytes) and a terabyte (TB)
is 1024 GB (1099511627776 bytes). A petabyte (PB) would be
1024 times as large, namely 1125899906842624 bytes
(9007199254740992 bits or 86.2 nJ/K).
The situation may be quite confusing for several reasons.
In particular, a few commercial designations have wrongly
ignored the above binary-based convention (powers of 1024)
and used the standard decimal one (powers of 1000) in some cases.
Even worse, the two have been mixed to create a special type of digital macaronic
terms like the "megabyte of storage" which turns out to be worth 1024000 bytes,
but is only used commercially for some removable storage media.
This came about (sadly) when the capacity of
the so-called 3½" IBM microfloppies
doubled from 720 kB to 1440 kB
and the larger capacity was widely advertised as "1.44 MB"
(instead of "1.40625 MB" or "1.4 MB").
In December 1998, the International Electrotechnical Commission (IEC)
attempted to clear up the situation by introducing a
kilobinary system,
in which we would no longer use kilobyte to designate 1024 bytes,
but kibibyte (KiB).
The IEC proposal is slowly
gaining some ground.
However, it should only be a way to disambiguate the customary exception which has been
universally used for multiples of the bit (b) and the 8-bit byte (B),
as far as addressable computer memory is concerned.
Ideally, acceptance of the IEC
proposal should only replace "kB" or "K" by "KiB" to mean 1024 bytes.
It should never be construed as the permission to use "kB"
concurrently to mean 1000 bytes.
(Current usage does not allow unrestricted use
of metric prefixes anyway:
It's not permissible to use "kiloinch" for 25.4 m, is it?)
Otherwise, ambiguity and confusion would be increased, not decreased.
Arguably, manufacturers of digital storage who use the abbreviation "GB"
for 1000 000 000 bytes would still be shortchanging their customers by
7.4%, even if the unambiguous IEC binary prefixes gain wider acceptance.
Warning: 1 kb/s = 1 Kib/s = 1.024 kbps
Be very aware that the binary exception only
applies to multiples of the bit and not
to derived units like the "bps" (bit per second),
so that 56 kbps is exactly 56000 bps.
This may not look so bad until you realize that a transfer speed of
"1 kilobit per second" is actually equal to 1.024 kbps,
so that the latter should only be pronounced "kilo-bee-pee-ess"
to avoid confusion with the former!
That's the current mess we've built for ourselves.
Careless standardization efforts could make the situation even worse
before it gets better.
"Brontobyte" [ hoax alert ]
This unit is just a joke
(2004)
nothing more! Unfortunately, the word caught the
fancy of
many unsuspecting webmasters
and is now often listed
among "serious" units of information
(even more dubious is the geobyte
of 1024 brontobytes).
1 brontobyte =
(1024) 9 bytes =
9903520314283042199192993792 bits
In terms of entropy,
this huge amount of information is only 1.7668 J/K.
( L. K. of Owen, WI.
2000-10-10)
What has a density of 1 ?
Proper units (g/cc, lb/ft 3, etc.)
are used to express an absolute density.
A relative density is the ratio
of an absolute density to the absolute density of "water".
For the utmost precision,
it's important to specify what kind of "water" is meant.
For example, SMOW ("Standard Mean Ocean Water")
at its densest point (around 3.98°C) has an absolute density of about 0.999975 g/cc.
However, the accepted conversion factor between "absolute" and "relative" density
is 0.999972 g/cc !
This is one number which has acquired the
unofficial status of a defined exact conversion factor,
which has ultimately little to do with actual water or SMOW.
In other words, the short answer to this question is:
"Water."
A more precise (somewhat cynical) long answer is:
"Anything with an absolute density of exactly 0.999972 g/cc."
Videos:
7-Layer Density Tower
|
9 Layers
|
Density Rainbow
|
Soda Density
|
Astronomical Densities
(Michael of United Kingdom.
2001-02-12)
What's the difference between normal [1N] and molar [1M] solutions in acid chemistry?
Particularly for sulfuric acid.
Each liter of a molar solution (1M or 1000mM) contains a mole of a given compound
(a mole of H2SO4
is about 98.08 grams of it).
A normal acid (1N), on the other hand, contains the solute(s)
that could produce a mole of H+ ions.
In the case of sulfuric acid, you'd have 2 H+
ions per molecule,
so that a normal (1N) solution of sulfuric acid is actually a 1/2 molar solution
(0.5M or 500mM).
A mole of "objects" [atoms, molecules, ions, electrons]
is defined to be as many of these as there are atoms in 12 grams of carbon-12.
The "number of things per mole of stuff" is a universal constant known as
Avogadro's Constant :
6.022 141 99(47)´1023 per mole.
[Here, the parenthesized 47 indicates an uncertainty whose standard deviation is
47 times the weight of the last decimal position shown.]
Free protons (H+ ions) in water are mostly a convenient
fiction, since such ions would quickly combine with nearby molecules of water to form
hydronium ions.
The dissociation of water molecules into ions
is thus best described by the following reversible chemical reaction:
2 H2O
«
H3O+ +
OH-
(J. M. of College Station, TX.
2001-02-11)
How much energy is required to raise the temperature
of one kilogram of water [by] one degree Celsius?
If the calorie was still defined as the energy required to raise
a gram of water by 1°C,
the answer to this question would be "1000 calories" (or 1 kcal).
However, the historical definition of the calorie was dependent on the starting temperature
and it's been deprecated.
Since 1935, the current (thermochemical)
calorie has been defined as
exactly 4.184 J.
In 1956, a competing definition gave rise to a slightly different "calorie" unit:
The "IT calorie" is 4.1868 J
(IT or IST stands for "International [Steam] Table").
This conversion factor is consistent with the definition of the Btu
(British thermal unit)
adopted at the 5th International Conference on the Properties of Steam
(London, July 1956),
which equates 1 Btu/lb and 2326 J/kg
(incidentally, a therm is 100000 Btu).
The Btu had an historical definition similar to that of the calorie:
In 1876, it was defined as the energy required to raise the temperature
of one pound (lb) of water by 1°F,
from the point of maximum density [around 3.98°C].
All told, it's best to reserve the 1956 IST definition to the Btu
(1 Btu is 1055.05585262 J, namely the ratio of the pound to the kilogram
multiplied by 2326 J) and use the standard 1935 thermochemical definition
for the calorie (1 cal is 4.184 J).
Unfortunately, you may also encounter a "thermochemical Btu"
(» 1054.35 J)
and an "IST calorie" (4.1868 J = 2326 * 0.0018 J).
The fifteen degree calorie
(also known as gram-calorie or "g-cal")
is still defined as the energy which raises a gram of water from
14.5°C to 15.5°C.
It has been measured to be equal to 4.1855 J
(with an uncertainty of 0.0005 J).
The energy which raises a kg of water by 1°C
is thus "about 4185.5 joules".
cdw239
(2001-08-23)
What is the equation for converting horsepower to watts?
The horsepower and the watt are both units of power;
there's just a conversion factor between them.
The way power is delivered (voltage, etc.) is irrelevant.
A horsepower (hp) is about 745.7 watts (W),
but many metric countries use another
closely related unit [best abbreviated "ch"]
which is nearly 735.5 W.
The horsepower unit (hp) was originally defined by James Watt (1736-1819)
as exactly equal to 550 ft-lbf per second (lbf = "pound-force", see below).
Since January 1, 1959,
the foot and the pound have been defined in metric terms
(1 ft = 0.3048 m and 1 lb = 0.45359237 kg, both exactly).
Furthermore, since the third CGPM of 1901, the standard
(or conventional)
acceleration of gravity has been defined as exactly equal to 9.80665 m/s2,
which is thus the "conversion factor" to use to transform units of mass
(like the pound, lb) into their common namesakes as units of force
(pound-force, lbf):
1 lbf is (0.45359237)(9.80665),
or 4.4482216152605 N exactly.
Multiply this by the length corresponding to 550 ft
(exactly 167.64 m) and you have the equivalence of a
horsepower in watts (since a watt "W" is simply a meter-newton per second),
namely 1 hp = 745.69987158227022 W exactly.
There's (almost) no need to say that everybody
usually rounds this up in the most obvious way:
1 hp » 745.7 W.
In countries where the metric system has been around for a while,
the horsepower (ch) is a 1.37% smaller unit,
called Pferdestärke (PS) in German,
paardekracht (pk) in Dutch,
hästkraft (hk) in Swedish,
caballo de vapor (CV) in Spanish,
cavalo-vapor in Portuguese,
cavalli vapore in Italian...
The French call it cheval-vapeur (ch)
or simply cheval (plural is chevaux).
This "metric" horsepower (ch) is defined as
75 kgf-m/s, which
engineers used to abbreviate as 75 kgm/s, using the obsolete symbol kgm
for a "technical" unit of energy called kilogrammetre or
kilogram-meter and worth 9.80665 J
(that same unit of energy was also called kilopond-meter
and abbreviated kpm ).
A metric horsepower (ch) is thus (75)(9.80665),
or exactly 735.49875 W.
French readers should not confuse this cheval-vapeur (ch) unit
with the French cheval fiscal (CV) which is
a nonlinear rating of a motor vehicle for tax purposes
(registration cost is about $30 per CV, as of this writing).
The CV rating, or fiscal power [sic], is
(P/40)1.6+ U/45,
where P is the maximum DIN power (in kW)
and U is the amount of CO2 emitted per unit of distance (in g/km).
From 1909 to 1947, British car taxation
was based on another unphysical rating called
RAC
horsepower (introduced by
the Royal Automobile Club ) numerically
equal to 0.4 times the square of the bore
(the diameter of each cylinder in inches) multiplied by the number of
cylinders. Several generations of British engines had
artificially long strokes which produced a larger
displacement (in cubic inches) for the same tax rating.
The assumption behind the RAC formula was that short stroke
engines would work at higher rpm: The maximum product of stroke and rpm
was taken to be a constant (6000 in/min) equal to
half the largest acceptable mean piston speed,
(estimated to be 1000 ft/min).
Paying no attention to British
tax law, American automakers designed
short stroke engines.
Adding to the confusion, a so-called electric horsepower
is defined as exactly equal to 746 W
(it's clearly a rounded-up version of the "hp").
Finally, there's an unrelated unit of power called the
boiler horsepower,
defined in 1884 as the power it takes to boil 34.5 lb of water per hour
(under 1 atm, when water is already at 100°C = 212°F).
So defined, the boiler horsepower is approximately
9809.91 W, or about 13.155 hp.
However, this is so close to 1000 kgf-m/s
(which is 9806.65 W) that I suspect
such a "metric" definition of the boiler horsepower may have been given...
(The quotes around "metric" are a reminder that "technical" units of force,
named after units of mass, are not official SI units.)
I'd be grateful if anyone could
tell me
if this is so...
(2001-05-04)
Why is 9.80665 m/s2 [1 G] the standard acceleration of gravity?
To an actual measurement of 9.80991 m/s2 in Paris,
a theoretical correction factor of 1.0003322 was applied which gives
a sea-level equivalent at 45° of latitude.
The result (9.80665223...) was rounded to five decimals
to obtain the value officially enacted by the third CGPM, in 1901.
The
above includes a centrifugal
component due to the rotation of the Earth,
whereas the gravitational field
at altitude zero has a slightly larger value,
used when tracking satellites outside
the atmosphere in nonrotating coordinates
(9.82025048(2) m/s2 )
which is the ratio of the Earth's gravitational constant
(3.986004415(8) 1014 m3/s2 )
to the square of the conventional radius of the Earth
(R = 6371000 m).
|
robster
(
"
and the numeral "1". When typing, a cursive
"
On 2001-10-26, 
