1. Measurements are necessary for experiments, production, and quality control. Standard units are needed to make measurements reliable, accurate, and uniform for all. 2. The CGS, MKS, and SI systems define standard units for measurements of length, mass, and time. The SI system is now accepted internationally. 3. Accuracy refers to how close a measurement is to the true value, while precision refers to the consistency of repeated measurements. Errors are the differences between measured and actual values.

1. UNITS & MEASUREMENT
1.NEED FOR MEASUREMENT:
Measurement is that operation by which we compare a physical quantity with a unit
chosen for that quantity. In science and engineering, we perform experiments. During
experiments, we have to take readings. Thus all these experiments require some
measurements to be made. During the production of mechanical products, we have to
measure the parts so as to find whether the part is made as per the specifications. Thus
measurements are necessary for production and quality control.
2.NEED OF UNIT:
we need standard unit for measurement to make our judgement more reliable and accurate. For
proper dealing, measurement should be same for everybody. Thus there should be uniformity in
measurement. For the sake of uniformity we need a common set of units of measurement, which are
called standard units. Nowadays Si units in science and technology almost accepted universally.

2. 3.UNIT
A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is
used as a standard for measurement of the same kind of quantity.
4.What are the requirements for a standard of units ?
Units that we measure depends on the frame of reference. For that without a standard unit the length of 1 km will
be different with respect to place. Then people more specifically scientists will face many problems in measuring
some quantity. So to avoid such type of confusion and problems one standard unit is needed which is applicable in
every parts of world.
5.What are CGS, MKS, FPS, SI Systems of Units?
CGS System of Units
In these types of systems of units, length, mass and time are to be measured in centimeter, gram, and second
respectively.
That means in the CGS system of units, The unit of length in centimeter, the unit of mass is gram and the unit of
time is second.
MKS System of Units
In this type of system of the unit, length, mass, and time are to be measured in meter, kilogram, and second
respectively.
That means in the MKS system of units, The unit of length is meter, the unit of mass is kilogram and the unit of
time is second.

3. 6.SI System of Units
This is the most important type of system of units.
FULL FORM : Standard International system of units.
This system of units is accepted all over the world internationally and being used.
The seven basic units in these types of system of units are shown in the figure such as meter, kilogram, ampere,
second, etc.

4. 7.Types of System of Units
•Basically, there are two types of system of units classified.

5. 8.DIMENSIONAL ANALYSIS
Dimensional analysis is the use of a set of units to determine the form of an equation or to ensure that the result of a
computation is correct. To present the values of most physical quantities, a unit is absolutely essential.
Quantity Unit Dimension Symbol
Length Metre (m) [L]
Time Second (s) [T]
Mass Kilogram (kg) [M]
Current Amp (A) [I]
Temperature Kelvin (k) [O]
The principle of homogeneity of dimensions states that an equation is dimensionally correct if
the dimensions of the various terms on either side of the equation are the same.
Example 1: Check the correctness of physical equation s = ut + ½ at2. In the equation, s is the displacement, u is the
initial velocity, v is the final velocity, a is the acceleration and t is the time in which change occurs.
Solution:
We know that L.H.S = s and R.H.S = ut + 1/2at2
The dimensional formula for the L.H.S can be written as s = [L1M0T0] ………..(1)
We know that R.H.S is ut + ½ at2 , simplifying we can write R.H.S as [u][t] + [a] [t]2
[L1M0T-1][L0M0T-1] +[L1M0T-2][L0M0T0]
=[L1M0T0]………..(2)
From (1) and (2), we have [L.H.S] = [R.H.S]
Hence, by the principle of homogeneity, the given equation is dimensionally correct.

6. 9.LIMITATION
•It doesn’t give information about the dimensional constant.
•The formula containing trigonometric function, exponential functions, logarithmic function, etc. cannot be derived.
•It gives no information about whether a physical quantity is a scalar or vector.
10.ACCURACY
The ability of an instrument to measure the accurate value is known as accuracy. In other words, it is the closeness
of the measured value to a standard or true value. Accuracy is obtained by taking small readings.
11.PRECISION
The closeness of two or more measurements to each other is known as the precision of a substance. If you weigh a
given substance five times and get 3.2 kg each time, then your measurement is very precise but not necessarily
accurate. Precision is independent of accuracy.
12.ERROR
An error may be defined as the difference between the measured and actual values. For example, if the two
operators use the same device or instrument for measurement. It is not necessary that both operators get similar
results. The difference between the measurements is referred to as an ERROR.

7. Accuracy Precision
Accuracy refers to the level of agreement
between the actual measurement and the
absolute measurement.
Precision implies the level of variation that lies in
the values of several measurements of the same
factor.
Represents how closely the results agree with the
standard value.
Represents how closely results agree with one
another.
Single-factor or measurement are needed.
Multiple measurements or factors are needed to
comment about precision.
It is possible for a measurement to be accurate
on occasion as a fluke. For a measurement to be
consistently accurate, it should also be precise.
Results can be precise without being accurate.
Alternatively, the results can be precise and
accurate.
13.ERROR CALCULATION
(a).Absolute Error
The difference between the measured value of a quantity and its actual value gives the absolute error. It is the
variation between the actual values and measured values. It is given by
Absolute error = |VA-VE|
(b).Percent Error
It is another way of expressing the error in measurement. This calculation allows us to gauge how accurate a
measured value is with respect to the true value. Per cent error is given by the formula
Percentage error (%) = (VA-VE) / VE) x 100

8. (c).Relative Error
The ratio of the absolute error to the accepted measurement gives the relative error. The relative error is given by
the formula:
Relative Error = Absolute error / Actual value
14.RULES AND IDENTIFICATION OF SIGNIFICANT FIGURES
The term “significant figures” refers to the number of important single digits (0 to 9 inclusive) in the coefficient of
expression in the scientific notation. The number of significant figures in the expression indicates the confidence
or precision with which an engineer or scientist indicates a quantity.
Significant Figures Examples
The numbers in boldface are the significant figures.
•4308 – 4 significant figures
•40.05 – 4 significant figures
•470,000 – 2 significant figures
•4.00 – 3 significant figures
•0.00500 – 3 significant figures

9. Significant Figures Rules
There are certain rules which need to be followed to measure the significant figures of a calculated
measurement.
Listed below are the basics of the law:
•All non-zero digits are significant.
•Zeroes between non-zero digits are significant.
•A trailing zero or final zero in the decimal portion only are significant.
Following are the significant figures rules that govern the determination of significant figures:
1.Those digits which are non-zero are significant.
For example, in 6575 cm there are four significant figures and in 0.543 there are three significant
figures.
2.If any zero precedes the non-zero digit then it is not significant. The preceding zero indicates the
location of the decimal point, in 0.005 there is only one and the number 0.00232 has 3 figures.
3.If there is a zero between two non-zero digits then it is also a significant figure.
For example; 4.5006 has five significant figures.
4.Zeroes at the end or on the right side of the number are also significant.
For example; 0.500 has three significant figures.
5.Counting the number of objects for example 5 bananas and 10 oranges have infinite figures as
these are inexact numbers.
-: NOTE : DO NUMERICAL BY YOURSELF :-