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Units

Unit: A unit of measurement is a definite magnitude of a physical quantity, defined and adopted by convention and/or by law, that is used as a standard for measurement of the same physical quantity. Any other value of the physical quantity can be expressed as a simple multiple of the unit of measurement.


For example, length is a physical quantity. The metre is a unit of length that represents a definite predetermined length. When we say 10 metres (or 10 m), we actually mean 10 times the definite predetermined length called "metre".

The SI or International System of Units is universally adopted system to measure physical quantities.

SI base units: There exists 7 SI base units, definition of these units given below. All units called ‘derived units’ are derived from SI base units.

The meter (abbreviation, m) - The meter is the SI unit of displacement or length. One meter is the distance traveled by a ray of electromagnetic (EM) energy through a vacuum in 1/299,792,458 (3.33564095 x 10 -9) second. The meter was originally defined as one ten-millionth (0.0000001 or 10 -7 ) of the distance, as measured over the earth's surface in a great circle passing through Paris, France, from the geographic north pole to the equator.

The kilogram (abbreviation, kg)- The Kilogram is the SI unit of mass. It is defined as the mass of a particular international prototype made of platinum-iridium and kept at the International Bureau of Weights and Measures. It was originally defined as the mass of one liter (10 -3 cubic meter) of pure water.

The second (abbreviation, s or sec)- The Second is the SI unit of time. One second is the time that elapses during 9.192631770 x 10 9 cycles of the radiation produced by the transition between two levels of Cesium-133 or Cs-133. It is also the time required for an EM field to propagate 299,792,458 (2.99792458 x 10 8 ) meters through a vacuum.

The kelvin (abbreviation K)- The kelvin also called the degree Kelvin (abbreviation, o K), is the SI unit of temperature. One Kelvin is 1/273.16 (3.6609 x 10 -3 ) of the thermodynamic temperature of the triple point of pure water (H2O).

The ampere (abbreviation, A)- The ampere is the SI unit of electric current. One ampere is the current that would produce a force of 0.0000002 (2 x 10-7 ) Newton between two straight, parallel, perfectly conducting wires having infinite length and zero diameter, separated by one meter in a vacuum. One ampere represents 6.24 x 10 18 unit electric charge carriers, such as electrons, passing a specified fixed point in one second.

The candela (abbreviation, cd)- The Candela is the SI unit of luminous intensity. It is the electromagnetic radiation, in a specified direction, that has an intensity of 1/683 (1.46 x 10 -3 ) watt per steradian at a frequency of 540 terahertz (5.40 x 10 14 hertz).

The mole (abbreviation, mol)- The mole is the SI unit of material quantity. One mole is the number of atoms in 0.012 kilogram of the most common isotope of elemental carbon (C-12). This is approximately 6.022169 x 10 23 , and is also called the Avogadro constant.

SI derived units include the hertz , the newton , the pascal (unit of pressure or stress) , the ohm , the farad , the joule , the coulomb , the tesla , the lumen , the becquerel , the siemen , the volt , and the watt .


Derived Units of the International System (SI)


Following are links to the definitions of these 22 units. The third column shows how each unit is derived from the preceding units, and the fourth column gives the formal equivalence of the unit in terms of the base units.


Derived Unit
Measures
Derivation
Formal Definition
Hertz (Hz)
frequency
/s
s-1
newton (N)
force
kg·(m/s2)
kg·m·s-2
pascal (Pa)
pressure
N/m2
kg·m-1·s-2
joule (J)
energy or work
N·m
kg·m2·s-2
watt (W)
power
J/s
kg·m2·s-3
coulomb (C)
electric charge
A·s
A·s
volt (V)
electric potential
W/A
kg·m2·s-3·A-1
farad (F)
electric capacitance
C/V
kg-1·m-2·s4·A2
ohm (omega)
electric resistance
V/A
kg·m2·s-3·A-2
siemens (S)
electric conductance
A/V
kg-1·m-2·s3·A2
weber (Wb)
magnetic flux
V·s
kg·m2·s-2·A-1
tesla (T)
magnetic flux density
Wb/m2
kg·s-2·A-1
henry (H)
inductance
Wb/A
kg·m2·s-2·A-2
degree Celsius (°C)
temperature
K - 273.15
K
radian (rad)
plane angle

m·m-1
steradian (sr)
solid angle

m2·m-2
lumen (lm)
luminous flux
cd·sr
cd·sr
lux (lx)
illuminance
lm/m2
cd·sr·m-2
becquerel (Bq)
activity
/s
s-1
gray (Gy)
absorbed dose
J/kg
m2·s-2
sievert (Sv)
dose equivalent
Gy·(multiplier)
m2·s-2
katal (kat)
catalytic activity
mol/s
mol·s-1


The term derived unit covers any algebraic combination of the base units, but it is only the 22 combinations listed above that have approved special names. For example, the SI derived unit of momentum (mass times velocity) has no special name; momentum is stated in kilogram meters per second (kg•m/s) or in newton seconds (N•s). A few SI derived units do have special names that have been defined but not approved. Here are some examples:


Derived Unit
Measures
Derivation
stere (st)
volume
m3
diopter (dpt)
refractive power
m-1
thermal ohm
thermal resistance
K/W
poiseuille (Pl)
dynamic viscosity
Pa·s
rayl
sound impedance
Pa·s/m
acoustic ohm
sound resistance
Pa·s/m3
daraf
electric elastance
F-1
talbot
luminous energy
lm·s
nit (nt)
luminance
cd/m2
molal
chemical concentration
mol/kg


Some practical units of Length, Mass and Time


Length:
•    1 light year = distance traveled by light in year in vacuum

•    1 ly = 9.46x10 15 m

•    1 Parsec = 3.26 ly

•    1 seamile or nautical mile = 6020 ft

•    1 micron (m) = 10-6m

•    1 Angstrom (A) = 10 -15 m

Mass

•    1 quintal = 100 kg

•    1 metric ton = 1000 kg

•    1 atomic mass unit or amu or Dalton = 1.66 x 10 -27 kg

•    1 slug = 14.59 kg

•    1 pound = 0.4537 kg

•    1 Chandrashekhar Limit = 1.4times the mass of Sun = 208 x 10 30 kg

Time


•    1 Solar day = 86400 sec
•    1 year  = 365.5 days
•    1 lunar month = 27.3 solar days
•    Tropical Year = This is the year when Solar eclipse occurs
•    Leap Year = It is the year when month of February happens to be 29 days.


Prefixes Used in Metric System


There are twenty prefixes officially specified by SI.



Prefix
Symbol
1000m
10n
Decimal
Short scale
Long scale
Since
yotta
Y
10008
1024
1000000000000000000000000
septillion
quadrillion
1991
zetta
Z
10007
1021
1000000000000000000000
sextillion
trilliard
1991
exa
E
10006
1018
1000000000000000000
quintillion
trillion
1975
peta
P
10005
1015
1000000000000000
quadrillion
billiard
1975
tera
T
10004
1012
1000000000000
trillion
billion
1960
giga
G
10003
109
1000000000
billion
milliard
1960
mega
M
10002
106
1000000
million
1960
kilo
k
10001
103
1000
thousand
1795
hecto
h
10002/3
102
100
hundred
1795
deca
da
10001/3
101
10
ten
1795

10000
100
1
one
deci
d
1000−1/3
10−1
0.1
tenth
1795
centi
c
1000−2/3
10−2
0.01
hundredth
1795
milli
m
1000−1
10−3
0.001
thousandth
1795
micro
μ
1000−2
10−6
0.000001
millionth
1960
nano
n
1000−3
10−9
0.000000001
billionth
milliardth
1960
pico
p
1000−4
10−12
0.000000000001
trillionth
billionth
1960
femto
f
1000−5
10−15
0.000000000000001
quadrillionth
billiardth
1964
atto
a
1000−6
10−18
0.000000000000000001
quintillionth
trillionth
1964
zepto
z
1000−7
10−21
0.000000000000000000001
sextillionth
trilliardth
1991

y
1000−8
10−24
0.000000000000000000000001
septillionth
quadrillionth
1991