Measurements and Units
(Calvin of Farina, IL.
20001105) 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 

10^{33}  
una, vendeka (V) 
10^{30}  
dea, weka (W) 
10^{27}  
nea, xenna (X) 
yotta  Y 
10^{24}  Adopted in 1991. 
otta 
zetta  Z 
10^{21}  Adopted in 1991. 
hepa 
exa  E  10^{18} 
Adopted in 1975. 
peta  P  10^{15} 
Adopted in 1975. 
tera  T  10^{12} 
Adopted in 1960.  megamega (MM) 
giga  G  10^{9} 
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) 
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
10^{18}=1000^{6},
whereas peta (Greek pente, 5) was picked to represent
10^{15}=1000^{5}.
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 (1000^{7}), and
yotta (1000^{8});
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.
[20030622 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 (20020501) :
Usenet
Archives show
Alejandro LópezOrtiz
posting 3 times, between 1998 and 2000,
a bogus list of prefixes ["7.5" dated 19980220]
whose previous version ["7.1", dated 19951231, last posted 19961009]
didn't include any bogus information...
In a 20020114 post,
Robi Buecheler plagiarized the above
text...
On 20041214, Robi Buecheler
apologized:[...]
I should have given you credit [and/or posted a] link.
Sorry. 
(J. B. of New Lenox, IL.
20010209)
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.
The situation may be quite confusing for several reasons.
In particular, a few commercial designations have wrongly
ignored the above binarybased 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 socalled 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).
This proposal has failed so far; we've never seen this in actual use!
Building on the accepted convention that "b" is for
bit and "B" is for byte (8 bits),
some individuals keep proposing the use a lowercase "k" for 1000
and an uppercase "K" for 1024.
For now, this must be rejected for several reasons:
The idea applies only to written text,
cannot be generalized to other commonly used prefixes,
and is in direct conflict with the current usage described above...
[Note also that "K" by itself denotes a kilobyte, kB, 1024 bytes or 8192 bits.]
Within a specific technical document,
ambiguities could conceivably be lifted by stating first
what is meant (e.g., "k=1000, K=1024") before using compound prefixes
like:
kk (for 1000000), kK (for 1024000) or KK (for 1048576).
Warning: 1 kb/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 "kilobeepeeess"
to avoid confusion with the former!
That's the current mess we've built for ourselves.
Any misguided standardization efforts could very well make the situation even worse
before it gets better.
( L. K. of Owen, WI.
20001010)
What has a density of 1 ?
Proper units (g/cc, lb/ft^{ 3}, etc.)
are used to express an absolute density,
whereas a relative density is defined as the ratio
of an absolute density to the absolute density of "water".
When top precision is called for,
it would be 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
(unofficially at least) the 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."
Note:
The original batch of SMOW came from seawater collected
by Harmon Craig on the equator at 180 degrees of longitude.
After distillation, it was enriched with heavy water
to make the isotopic composition match what would be expected of undistilled seawater
(distillation changes the isotopic composition,
because lighter molecules are more volatile).
In 1961, Craig tied SMOW to the NBS1 sample
of meteoric water originally collected from the Potomac River
by the National Bureau of Standards
(now NIST).
For example, the ratio of Oxygen18 to Oxygen16 in SMOW was
0.8% higher than the corresponding ratio in NBS1.
This "actual" SMOW is all but exhausted, but water closely matching its
isotopic
composition has been made commercially available, since 1968,
by the Viennabased IAEA
(International Atomic Energy Agency) under the name of VSMOW or "Vienna SMOW".
(Michael of United Kingdom.
20010212)
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 H_{2}SO_{4}
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 carbon12.
The "number of things per mole of stuff" is a universal constant known as
Avogadro's Constant :
6.022 141 99(47)´10^{23} per mole.
[Here, the parenthesized 47 indicates an uncertainty whose standard deviation is
47 times the weight of the last decimal position shown.]
(J. M. of College Station, TX.
20010211)
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 gramcalorie or "gcal")
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
(20010823)
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 (17361819)
as exactly equal to 550 ftlbf per second (lbf = "poundforce", 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/s^{2},
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
(poundforce, 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 meternewton 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,
cavalovapor in Portuguese,
cavalli vapore in Italian...
The French call it chevalvapeur (ch)
or simply cheval (plural is chevaux).
This "metric" horsepower (ch) is defined as
75 kgfm/s, which
engineers used to abbreviate as 75 kgm/s, using the obsolete symbol kgm
for a "technical" unit of energy called kilogrammetre or
kilogrammeter and worth 9.80665 J.
A metric horsepower (ch) is thus (75)(9.80665),
or exactly 735.49875 W.
French readers should not confuse this chevalvapeur (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 CO_{2} emitted per unit of distance (in g/km).
Adding to the confusion, a socalled electric horsepower
has also been defined as exactly equal to 746 W
(it's clearly a roundedup 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 kgfm/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...
(20010504)
Why is 9.80665 m/s^{2} [1 G] the standard acceleration of gravity?
To an actual measurement of 9.80991 m/s^{2} in Paris,
a theoretical correction factor of 1.0003322 was applied which gives
a sealevel 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 value includes a centrifugal
component due to the rotation of the Earth,
whereas the value of the gravitational field
at altitude zero is equal to 9.82025048(2) m/s^{2}.
Such a larger value is relevant when tracking satellites outside
the atmosphere in nonrotating coordinates.
It's simply the ratio of the Earth's gravitational constant
(3.986004415(8) 10^{14 }m^{3}/s^{2 })
to the square of the conventional radius of the Earth
(R = 6371000 m).
