# Units and measurement

The 14th general conference on weight and measurement in 1971 decided seven fundamental quantities as basic quantities. These seven unit of measurement are known as the International System of units along with two supplementary units. Its abbreviated as SI from its french name. This system of unit is mostly used by most of the book and has been in use throughout the world extensively.

S.No. Quantity SI unit Symbol
1 Length meter m
2 Mass kilogram kg
3 Time second s
4 Electric current ampere A
5 Temperature kelvin K
6 Amount of substance mole mole
7 Luminous intensity candela cd

Meter: One meter is distance between two lines on a platinum iridium bar kept at zero degree Celsius at International Bureau of Weights and Measurements at Sevres, Paris. A more accurate definition of meter is the distance traveled by light in vacuum in $\frac{1}{2997922458}$ second.

Kilogram: A standard kilogram is an agreed upon mass of cylinder made up off platinum iridium alloy kept at International Bureau of Weights and Measurements in Paris.

Second: One second is defined as the time taken to make 9,192,631,770 vibrations by a hyperfine transitions in Cesium-133 atom.

Kelvin: It is $\frac{1}{273.15}$ of the temperature of triple point of water. The temperature of triple point of water is 273.15 Kelvin.

Mole: Mole is defined as the mass of the substance that contains $6.02252 \times 10^{23}$ number of atoms or molecules. The number $6.02252 \times 10^{23}$ is called Avogadro number.

Candela: It is the luminous energy emitted per second by a source per unit solid angle. It has a radiant intensity of $\frac{1}{683}$ watt per steradian.

Radian: It is an angle subtended at the center of a circle of radius r by an arc of length r of the same circle.

$1 radian = \frac{Arc}{radius}$

Note that: $2\pi radians = 360 degree$

Solid angle: It is the angle subtended at a point by the surface area.

$Solid-angle = \frac{Area-of-surface}{(distance-of-point-from-the-surface)^2}$

$\Omega = \frac{A}{x^2}$

Steradian: It is the solid angle subtended at the center by unit area on the surface of a sphere of unit radius. Total solid angle subtended at the center by the surface area of a sphere of radius r is 4$\pi$ steradian.

Prefixes of power of Ten
S.No. Power of 10 Prefix Symbol
1 $10^{18}$ exa- E
2 $10^{15}$ peta- P
3 $10^{12}$ tera- T
4 $10^{9}$ giga- G
5 $10^{6}$ mega- M
6 $10^{3}$ kilo- k
7 $10^{2}$ hecto- h
8 $10$ deka- da
9 $10^{-1}$ deci- d
10 $10^{-2}$ centi- c
11 $10^{-3}$ milli- m
12 $10^{-6}$ micro- $\mu$
13 $10^{-9}$ nano- n
14 $10^{-12}$ pico- p
15 $10^{-15}$ femto- f
16 $10^{-18}$ atto- a