Units
To express the measurement of any physical quantity two things are considered:
(i) Its unit,
(ii) The numerical value.
Magnitude of a physical quantity = numerical value * unit
Units are of two types:
(i) Basic units
(ii) Derived units
(i) The basic or fundamental units are those of length (m), ass (kg), time (s), electric current (A), thermodynamic temperature (K), amount of substance (mol) and luminous intensity (cd).
(ii) Derived units are basically derived from the fundamental units, e.g., unit of density is derived from units of mass and volume.
The systems used for describing measurements of various physical quantities are
(a) CGS system It is based on centimetre, gram and second as the units of length, mass and time respectively.
(b) FPS system A British system which used foot(ft). pound (lb) and second (s) as the fundamental units of length, mass and time.
(c) MRS system Uses metre (m), kilogram (kg) and second (s) respectively for length, mass and time; ampere (A) was added later on for electric current.
(d) SI system (1960)International system of units and contains following seven basic and two supplementary units:
Base Physical Quantities and their Corresponding Basic Units
SUpplementary units It includes plane angle in radian and solid angle in steradian.
Prefixes
The SI units of some physical quantities are either too small or too large. To change the order of magnitude. these are expressed by using prefixes before the name of base units. The various prefixes are listed as
Dimensional Analysis
Often while calculating, there is a need to convert units from one system to other. The method used to accomplish this is called factor label method or unit factor method or dimensional analysis.
In this,
Information sought = Information given * Conversion Factor
Important Conversion Factor
Scientific Notation
In such notation, all measurements (however large or small) are expressed as a number between 1.000 and 9.999 multiplied or divided by 10. In general as
N * 10
Here, N is called digit term (1.000-9.999) and n is known as exponent. e.g., 138.42 cm can be written as 1.3842 * 102 and 0.0002 can be written as 2.0 * 10-4.
precision and Accuracy
Precision refers the closeness of the set of values obtained from identical measurements of a quantity. Precision is simply a measure of
reproducibility of an experiment.
Precision = individual value – arithmetic mean value
Accuracy is a measure of the difference between the experimental value or the mean value of a set of measurements and the true value.
Accuracy = mean value – true value
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