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Units

When a particular instrument indicates a reading, to specify the reading and use it in the further calculations, it is necessary to specify type and magnitude for that reading. The magnitude is nothing but the reading obtained on the instrument. The type of the reading is nothing but the unit of the physical quantity which is measured by the instrument. Without unit, only magnitude has no physical meaning. Thus the unit can be defined as follows: The standard measure of each type of physical quantity to be measured is called unit. The physical, chemical, electrical quantity, property, process, variable or a condition to be measured is referred as measurand. The measurement involves comparison of a quantity with a standard value.  

 

SI Units

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Number of systems of units have been used at various times in the past days. The different systems of units are available in the different countries. The M.K.S and C.G.S systems of units have been used in earlier days. However, for the sake of uniformity of units all over the world, an international organization, the General Conference of Weight and Measures, recommended a unified systematically constituted system of units, in 1960. This system of units is called SI (System International Units) system of units. The SI system of units is divided into three categories namely:

Fundamental Units:

The units which are independently chosen and not dependent on any other units are called fundamental units. These are also called base units. The seven such base units form the basis of SI system of units. These base units are metre, kilogramme, second, ampere, kelvin, mole, candela.


Supplementary Units:

In addition to the fundamental units, there are two supplementary units added to the SI system of units. These units are defined as:

1) Radian for the plane angles: The plane angle subtended by an arc of a circle equal in length to the radius of the circle. The radian is denoted as rad.

2) Steradian for the solid angles: The solid angle subtended at the centre of a sphere by the surface whose area is equal to the square of the radius of the sphere. The steradian is denoted as sr.


Derived Units:

The units other than fundamental and supplementary are derived from the fundamental and supplementary units. Hence these units are called derived units. The derived units can be mainly classified as:

1) Mechanical units such as mass, velocity, acceleration, force, weight, torque, work, energy, power etc.

2) Electric and Magnetic units such as power, energy, ohms, farads, henries, magnetic flux in webers, tesla etc.

3) Thermal units such as latent heat, specific heat capacity, sensible heat, calorific value etc.

There are number of other derived units available to specify the quantities like are, volume, density, luminous flux, luminance etc.

Accuracy and Errors in Measurement

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Accuracy is the degree of agreement of the measured value with the true value. The true value is frequently unknown and it is therefore impossible to determine the accuracy of a method using samples. The measurement means, to monitor a process or a operation and using an instrument, express the parameter, quantity or a variable in terms of meaningful numbers. Such a measurement gives in depth knowledge of the process and the parameter and helps in further modifications, if required. Thus the measurement provides us with a means of expressing a natural phenomena or the various processes, in quantitative terms.  The feedback information is possible with the help of measurement techniques, which helps in achieving goals and objectives of various engineering processes and systems. The measurement of a given parameter or quantity is the act or result of a quantitative comparison between a predefined standard and an unknown quantity to be measured. The major problem with any measuring instrument is the error. Hence, it is necessary to select the appropriate measuring instrument and measurement procedure which minimizes the error. The measuring instrument should not affect the quantity to be measured. The measuring instrument may be defined as a device for determining the value or magnitude of a quantity or variable. Thus measurement is a process by which one can convert physical parameters to meaningful numbers. The measurement confirms the validity of hypothesis and also adds to its understanding. The measurements helps in design of equipment and also in proper operation and maintenance of equipment.

Significant Figures and Order of Accuracy

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The accuracy of a number is specified by the number of significant figures it contains. A significant figure is any digit, including zero, provided it is not used to specify the location of the decimal point for the number. For example, the numbers begin or end with zeros, however, it is difficult to tell how many significant figures are in the number. Consider the number 400. Does it have one (4) or perhaps two (40) or three (400) significant figures? In order to clarify this situation, the number should be reported using powers of 10. Using engineering notation, the exponent is displayed in multiples of three in order to facilitate conversion of SI units to those having an appropriate prefix. Thus, 400 expressed to one significant figure would be 0.4 (103). Likewise, 2500 and 0.00546 expressed to three significant figures would be 2.50 (103) and 5.46 (10-3).

Rules to determine significant figures:
  • Zero is not a significant figure when it is the first figure in a number (eg. 0.00034 has only two significant figures). A zero in any other position is significant (eg. 102 has three significant figures). In order to avoid confusion it is preferable to use scientific notation when expressing results (eg. 6.20 * 10^4 has three significant figures).
  • When rounding off numbers, add one to the last figure retained if the following figure is greater than 5 (eg. 0.53257 becomes 0.5326 when rounded off to four significant figures).
  • Round 5 to the nearest even number (eg. 0.255 becomes 0.26 when rounded off to two significant figure). If the digit just before 5 is  even, it is left unchanged (eg. 0.345 becomes 0.34 when rounded off to two significant figures); if it is odd, its value is increased by one (eg. 0.335 becomes 0.34 when rounded off to two significant figures).
  • If two or more figures are present to the right of the figure to be retained, they are considered as a group (eg. 6.8[501] should be rounded off to 6.9; 7.4[499] should be rounded off to 7.4)
  • In addition  and subtraction the result should be reported to the same number of decimal places as there are in the number with the smallest number of decimal places.
  • In multiplication and division the result should have an uncertainty of the same order as the number with the greatest uncertainty.
  • In the logarithm of a number we retain the same number of digits to the right of the decimal point as there are significant figures in the original number.
  • In the antilogarithm of a number we retain as many significant figures as there are digits to the right of the decimal point in the original number.
More topics in Units
Unit Conversion Measurement Techniques
Dimensional Analysis and Vectors Conversion of Mass
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