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    Units and Measurement
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    Two gold pieces weigh 20.15 g and 20.17 g. What is the difference in the masses of the pieces to correct significant figures?
    Mass of  first piece = 20.15 g
    MAss of second piece = 20.17 g 

    Therefore,

    Difference in the masses of two pieces is,

    incrementm = (20.17 - 20.15) g

            = 0.02 g 

    Since the masses of pieces are known upto second decimal place of gm and difference is also upto second decimal place, hence the difference in the masses is 0.02 g.
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    Let a physical quantity X be measured in an experiment and the experiment be repeated for n times. If measured values are X1 X2......Xn then find the range in which all the measured values will lie.

    When there are 'n' measured values, we cannot take any value as the true value.

    Thus, true value is the mean of all the observed values.

    straight X space equals space fraction numerator straight X subscript 1 plus straight X subscript 2 plus......... space plus space straight X subscript straight n over denominator straight n end fraction 

    The absolute error in measured values is,

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    Now the mean absolute error is ,

    straight capital delta space straight X equals space fraction numerator ΔX subscript 1 plus ΔX subscript 2 plus.......... plus ΔX subscript straight n space over denominator straight n end fraction 

    This means absolute error is the maximum possible error in the measurement.

    Thus, all measured values of measurement lie in the range, 

    straight X plus-or-minus ΔX

    i.e., straight X minus ΔX space less than space straight X subscript 1 space less than space straight X space plus ΔX

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    What is the least count of a screw gauge, whose circular scale is divided into 100 equal parts and the pitch of the screw is 1 mm?

    Number of divisions on circular scale, N = 100
    Pitch of screw gauge is, d = 1 mm

    space space therefore Least count = straight d over straight N 

                            equals fraction numerator 1 mm over denominator 100 end fraction equals 0.01 space mm 

                            equals space fraction numerator 1 space mm over denominator 100 end fraction equals 0.01 mm
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    What is the order of the magnitude of the ratio of radius of the earth to the height of a building 5m high?

    We have,

    Radius of earth = 6.4 space straight x space 10 to the power of 6 space end exponent straight m 

    Height of building = 5 m

    Now, 

    fraction numerator Radius space of space the space earth over denominator Height space of space building space end fraction equals fraction numerator 6.4 space straight x space 10 to the power of 6 straight m over denominator 5 straight m end fraction
                              space space space space equals space 1.28 space straight x space 10 to the power of 6 almost equal to 10 to the power of 6

    So, ratio is of the order of magnitude = 6

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    Define the least count of screw gauge.
    Least count of screw gauge is the distance by which the screw advances when it is rotated by one division on the circular scale.

    Mathematically, it is given by

    Least count =  fraction numerator Pitch over denominator No. space of space div. space on space circular space scale end fraction
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