units , measurement , SI units, derived units

             UNITS OF MEASUREMENT 

    Many properties of matter are quantitative in nature. When you measure something, you are comparing it with some standard. The standard quantity is reproducible and unchanging.
      Many properties of matter such as mass, length, area, pressure, volume, time, etc. are quantitative in nature. Any quantitative measurement is expressed by a number followed by units in which it is measured. For example, length of class room can be represented as 10 m. Here 10 is the number and 'm' denotes metre-the unit in which the length is measured.The standards are chosen orbitrarily with some universally acceped criteria. ''The arbitrarily decided and universally accepted standards are called units.''
     There are several systems in which units are expressed such as
1.C.G.S. System :Length (centimetre), Mass (gram), Time (second)
2.M.K.S. System : Length (metre), Mass (kilogram), Time (second)
3.F.P.S. System : Length (foot), Mass (pound), Time (second)
4. S.I. System : The 11th general conference of weights and measures (October 1960) adopted International system of units, popularly known as the SI units. The SI has seven basic units from which all other units are derived called derived units. The standard prefixes which helps to reduce the basic units are now widely used.
Dimensional analysis :
 The seven basic quantities lead to a number of derived quantities such as pressure, volume, force, density, speed etc. The units for such quantities can be obtained by defining the derived quantity in terms of the base quantities using the base units. For example, speed (velocity) is expressed in distance/time. So the unit is m /s or 1ms-¹. The unit of force (mass×acceleration)  is kg ms-² and the unit for acceleration is ms-². 
                                             Seven basic SI units 

SI PREFIXES

We deal from very small (micro) to very large (macro) magnitudes, as one side we talk about the atom while on the other side of universe, e.g., the mass of an electron is 9.1 ×10‐³¹ kg while that of the sun is 2×10³⁰ kg. To express such large or smallmagnitudes we use the following prefixes :
                              SI prefixes for multiples and sub multiples of units.

Practical Units
(1) Length 
(i) 1 fermi = 1 fm = 10‐¹⁵m
(ii) 1 X-ray unit = 1XU = 10‐¹³m
(iii) 1 angstrom = 1Å = 10‐¹⁰ m = 10‐⁸cm =  10‐⁷  mm 
(iv) 1 micron  = 10‐⁶ m
(v) 1 astronomical unit = 1 A.U. = 1. 49 ×10¹¹ m ~1.5 ×10¹¹m ~10⁸km
(vi) 1 Light year = 1 ly = 9.46 × 10¹⁵m
(vii) 1 Parsec = 1pc = 3.26 light year
(2) Mass
(i) Chandra Shekhar unit : 1 CSU = 1.4 times the mass of sun = 2.8 ×10³⁰kg
(ii) Metric tonne : 1 Metric tonne = 1000 kg
(iii) Quintal : 1 Quintal = 100 kg
(iv) Atomic mass unit (amu) : amu = 1.67 × 10‐²⁷ kg
Mass of proton or neutron is of the order of 1 amu
(3) Time
(i) Year : It is the time taken by the Earth to complete 1 revolution around the Sun in its orbit.
(ii) Lunar month : It is the time taken by the Moon to complete 1 revolution around the Earth in its orbit. 1 L.M. = 27.3 days
(iii) Solar day : It is the time taken by Earth to complete one rotation about its axis with respect to Sun. Since this time varies from day to day, average solar day is calculated by taking average of the duration of all the days in a year and this is called Average Solar day. 

1 Solar year = 365.25 average solar day

or average solar day 1÷365.25the part of solar year

(iv) Sedrial day : It is the time taken by earth to complete one rotation about its axis with respect to a distant star. 1 Solar year = 366.25 Sedrial day  = 365.25 average solar day Thus 1 Sedrial day is less than 1 solar day.

(v) Shake : It is an obsolete and practical unit of time.1 Shake = 10‐⁸ sec

Derived units 

The base or fundamental SI units like length, mass, time, etc. are independent of each other. The SI units for all other physical quantities such as area, density, velocity can be derived in terms of the base SI units and are called derived units. In order to find the derived unit for a physical quantity we have to find out the relationship between the physical quantity and the base physical quantities. Then substitute the units of the base physical quantities to find the desired derived unit. 

Derived Quantities and Units:

Some commonly encountered physical quantities other than base physical quantities, their relationship with the base physical quantities and the SI units are given in below Table.
                 Some examples of derived SI units of the commonly used physical quantities.

 A number of physical quantities like force, pressure, etc. are used very often but their SI units are quite complex. Due to their complex expression it becomes quite inconvenient to use them again and again. The derived SI units for such physical quantities have been assigned special names. Some of the physical quantities whose SI units have been assigned special names are compiled in below Table

                        Names and symbols of the derived SI units with special names. 

Changing number into scientific notation 

Scientific notation , a given value is expresed as a number written with one non zero digit to the left of the decimal point and all other digits to the right of it. It takes more  than a quick glance at a number such as 0.0000076 in. to have any idea of uts magnitude. However, if the number is written as_7×10^-6 in., one can immediately gauge its value. when number require the use of many nonsignificant zeros, we express these in scientific notation. The number is multiplied by 10 raised to a given power, called the exponent. The exponent indicates the magnitude of the number . 

Following are some powers of 10 and their equivalent numbers. 

₁₀⁰ = 1                                                           ₁₀^-1= 1/10 =0.1

  ₁₀¹ = 10                                                 ₁₀^-2=1/₁₀²=0.01

 ₁₀²= 10×10 =100                                         ₁₀^-3=1/₁₀³=0.001

 ₁₀³=10×10×10=1000                                   ₁₀^-4=1/₁₀⁴=0.0001

  ₁₀⁴= 10×10×10×10=10,000                        etc. 

etc. 

A huge number that we will soon deal with is 602,200,000,000,000,000,000,000.

The way it is expressed , however, is in a much more readable form as follows

                                       _6.022×10²³

Here the number (6.022 known as coefficient) expresses the proper precision of four significant figures. This expression means that 6.022 is multiplied by   ₁₀²³ (which is 1 followed by 23 zeros).