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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