Units and Measurements
A number, along with a unit gives the measurement of a physical quantity. Though the number of physical quantities is very large, we only require a specific number of units for expressing all these quantities. These interconnected with each other. The units for the fundamental or basic quantities are known as fundamental units or base units. The rest of the physical quantities (non-fundamental quantities) can be expressed as combinations of the fundamental units. The units for the derived quantities are called derived units. A complete pack of the base units and derived units is known as the system of units. Three systems of units are widely used. They are the CGS system, the FPS (or British) system, and the MKS system.
Every physical quantity has a particular standard unit. Like for length, it is metre, for weight it is kilogram, etc.
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System
|
Length
|
Mass
|
Time
|
|
CGS
|
centimetre
|
gram
|
second
|
|
FPS
|
foot
|
pound
|
second
|
|
MKS
|
metre
|
kilogram
|
second
|
Table: 1.1
There are seven fundamental quantities. They are as follows:
- Time (second)
- Length (meter)
- Mass (kilogram)
- Electric Current (ampere)
- Temperature (kelvin)
- Amount of Substance (mole)
- Luminous Intensity (candela)
Besides the seven base units, two more units are defined for
(1) Plane Angle: Plane angle dθ is as the ratio of the length of arc ds to the radius r.
(2) Solid Angle: Solid angle d? is as the ratio of the intercepted area dA of the spherical surface about the apex (centre), to the square of the radius r.
The unit for plane angle is radian (rad), and the unit for the solid angle is steradian (sr). Both radian and steradian are dimensionless quantities.
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Physical Quantity
|
Name
|
Symbol
|
Definition
|
|
Length
|
Metre
|
m
|
The metre is the length of the path
covered by light in vacuum during a time
interval of 1/299,792,458 part of a
second.
|
|
Weight
|
Kilogram
|
Kg
|
The kilogram is equal to the mass of the
international prototype of the kilogram (a
platinum-iridium alloy cylinder) kept at
the International Bureau of Weights and
Measures, at Sevres, near Paris, France.
|
|
Time
|
Second
|
s
|
The second is the time duration of
9,192,631,770 periods of the radiation
corresponding to the transition between
the two hyperfine levels of the ground
state of the cesium-133 atom.
|
|
Electric Current
|
Ampere
|
Amp
|
The ampere is that constant current
which, if maintained in current two
straight parallel conductors of infinite
length, of negligible circular cross-
section, and placed 1 metre apart in vacuum, would produce between these
conductors a force equal to 2/10000000 newton
per metre of length.
|
|
Temperature
|
Kelvin
|
K
|
The kelvin is the fraction 1/273.16 of the
thermodynamic dynamic temperature of
the triple point of water.
|
|
Amount of Substance
|
Moles
|
mol
|
The mole is the amount of substance of a
system which contains substance as many
number of elementary particles as there
are atoms in 0.012 kilogram of carbon-
12.
|
|
Luminous Intensity
|
Candela
|
Cd
|
The candela is the luminous intensity in a
given intensity direction, of a source that
emits monochromatic radiation of
frequency 540 terahertz and that has a
radiant intensity in that direction of
1/683 watt per steradian.
|
Table: 1.2
Significant Figures:
- All non-zero digits are significant. For example in 567 m, there are three significant figures and in 0.98 cm, there are two significant figures.
- Zeros before first non-zero digit are not significant. Such zero denotes the position of the decimal point. For example in 0.09 has one significant figure and 0.000087 has two significant figures.
- The zeros between two non-zero digits are significant. Thus, 7.009 has four significant figures.
- The zeros at the end or right of a number are significant if they are on the right side of the decimal point. For example, 0.800 has three significant figures.
- Counting numbers for example, 5 pens have infinite significant figures as these are exact numbers and can be represented by writing infinite number of zeros after placing a decimal like 5 = 5.000000.
Addition and Subtraction:
The result cannot have more digits to the right of the decimal point than either of the original numbers.
Multiplication and Division:
The result cannot have more significant figures as are there in the measurement with the few significant figures.
Study Material