Unit Prefixes
unit prefixes  converting
units
Unit Prefixes
Many units are not convenient for using for all the uses we have for
them. For example, the metre is not long enough to conveniently use for
measuring long distances. The distance from Auckland to Tauranga is about
200,000 m. It is much more convenient to use a unit a thousand times as
big as the metre  a kilometre  so that we can say Auckland to Tauranga
is 200 km. Here "kilo" is a prefix to "metre" , and
means a thousand.
Prefixes also allow us to easily do slightly weird things, like express the number
of megaseconds in a year. (See the bottom of the page for the number.)
The capitalisation of prefixes is very important. More than a handful
of mA (milliamps) is enough to kill you, but a MA (megaamp) is enough
to blow you apart, while a Ma (megaannum) means something else again
(millions of years).
With all prefixes the accent is on the first syllable. Hence kilometer,
not kilometre.
The prefix always takes precedence over any exponentiation; thus "km^{2}"
means square kilometre and not kilo–square metre. For example, 3
km^{2} is equal to 3,000,000 m^{2} and not to 3,000 m^{2}
(nor to 9,000,000 m^{2}).
When using the symbol for a unit, an s is not added to the end
to signify plural forms. In other words "10 m" is not written
as "10 ms" because that then makes it "ten milliseconds".
The problem is perhaps most common with the units km and cm, since some
people think they are simply abbreviations, not symbols. Kilometreseconds
(kms) and centimetreseconds (cms) are really not very commonly used units.
The twenty SI (Système International) prefixes are shown in the
chart below.
SI prefixes
1000^{m} 
10^{n} 
Prefix 
Symbol 
Since^{[1]} 
Short scale 
Long scale 
Decimal 
1000^{8} 
10^{24} 
yotta 
Y 
1991 
Septillion 
Quadrillion 
1,000,000,000,000,000,000,000,000 
1000^{7} 
10^{21} 
zetta 
Z 
1991 
Sextillion 
Trilliard 
1,000,000,000,000,000,000,000 
1000^{6} 
10^{18} 
exa 
E 
1975 
Quintillion 
Trillion 
1,000,000,000,000,000,000 
1000^{5} 
10^{15} 
peta 
P 
1975 
Quadrillion 
Billiard 
1,000,000,000,000,000 
1000^{4} 
10^{12} 
tera 
T 
1960 
Trillion 
Billion 
1,000,000,000,000 
1000^{3} 
10^{9} 
giga 
G 
1960 
Billion 
Milliard 
1,000,000,000 
1000^{2} 
10^{6} 
mega 
M 
1960 
Million 
1,000,000 
1000^{1} 
10^{3} 
kilo 
k 
1795 
Thousand 
1,000 
1000^{2/3} 
10^{2} 
hecto 
h 
1795 
Hundred 
100 
1000^{1/3} 
10^{1} 
deca 
da 
1795 
Ten 
10 
1000^{0} 
10^{0} 
(none) 
(none) 
NA 
One 
1 
1000^{1/3} 
10^{1} 
deci 
d 
1795 
Tenth 
0.1 
1000^{2/3} 
10^{2} 
centi 
c 
1795 
Hundredth 
0.01 
1000^{1} 
10^{3} 
milli 
m 
1795 
Thousandth 
0.001 
1000^{2} 
10^{6} 
micro 
µ 
1960^{[2]} 
Millionth 
0.000 001 
1000^{3} 
10^{9} 
nano 
n 
1960 
Billionth 
Milliardth 
0.000 000 001 
1000^{4} 
10^{12} 
pico 
p 
1960 
Trillionth 
Billionth 
0.000 000 000 001 
1000^{5} 
10^{15} 
femto 
f 
1964 
Quadrillionth 
Billiardth 
0.000 000 000 000 001 
1000^{6} 
10^{18} 
atto 
a 
1964 
Quintillionth 
Trillionth 
0.000 000 000 000 000 001 
1000^{7} 
10^{21} 
zepto 
z 
1991 
Sextillionth 
Trilliardth 
0.000 000 000 000 000 000 001 
1000^{8} 
10^{24} 
yocto 
y 
1991 
Septillionth 
Quadrillionth 
0.000 000 000 000 000 000 000 001 
 The metric system was introduced in 1795 with six prefixes.
The other dates relate to recognition by a resolution of the CGPM.
 The 1948 recognition of the micron by the CGPM was abrogated
in 1967.

For more names of big numbers see names of large numbers.
Converting Units
As well as standard units, like metres and cubic meters, we have lots
of other units that are sometimes used instead, like (the old unit of)
feet and litres.
Converting from cubic metres to litres is easy, since the definition
of the litre comes from the metre, but we can also work out a volume
directly in litres by calculating the number of cubic decimeters in
an object. Remember, a litre is 1 dm^{3} which
is a cube 10 cm on a side.
For example, if we want to work out the volume in litres
of a mattress which is 900 mm wide by 100 mm thick by 1800 mm long we
could multiply these figures together (to make 162 million cubic millimetres)
then divide by one million, or we could much more simply make the calculations
using
decimetres. Remember:
1 m = 10 dm
1 dm = 10 cm
1 cm = 10 mm
9 dm x 1 dm x 18 dm = 162 dm^{3} = 162 L
To convert feet to metres – units which both describe length but do not
simply relate to each other – we need to know the conversion factor. From
the modern definition of an inch:
1 inch = 25.4 mm
12 inches = 1 foot
∴ 1 foot = 304.8 mm
∴ 1 m ≈ 39.37 inches or 3.28 feet
Calculating the number of seconds in a year is easier, as it's just a
matter of multiplying the right numbers together. (Don't forget to add
about a quarter of a day for leap years.*) Using a prefix allows us to express
it as the number of megaseconds in a year.
1 year
=
365.25 days
=
8766 hours
= 525,960 minutes
= 31,557,600 s
= 31,557.6 ks
= 31.5576 Ms
