2. UNITS & MEASUREMENT
Range of Lengths
1 fermi = 1f= 10 -15 m
1 angstrom = 1A0 = 10-10 m
1 astronomical Unit = 1.496 x 10 11 m
1 light year = 9.46 x 10 15 m
1parsec = 3.08 x10 16m Accuracy and Precision
Accuracy – It is the measure of how close the measured value is to the true
value of the quantity.
Precision – It tells to what resolution the quantity is measured.
3. TYPES OF ERRORS
1.Systematic Errors
The errors that tend to be in one direction, either positive or
negative.
Sources of systematic errors
a)Instrumental errors
b)Imperfection in experimental technique or procedure
c)Personal errors.
2.Random errors
Errors which occurs irregularly due to random and unpredictable fluctuations.
3.Least count error
Error associated with the resolution of the instrument is least count
errors.
Steps to minimise least count error
i) Using instruments of higher precision
ii) Improve experimental techniques
iii) Repeating the observations several times and taking the arithmetic mean.
4. ABSOLUTE ERROR, RELATIVE ERRORAND PERCENTAGE ERROR.
Absolute error: The magnitude of the difference between the true
value of the quantity and the individual measured value is called the
absolute error of the measurement
Suppose the values obtained in several measurements are a1, a2, a3...., an.
The arithmetic mean of these values is taken as the best possible
value(true value) of the quantity under the given conditions of
measurement
amean = (a1+ a2 + a3+...+ an) /n
Absolute errors of the measurement is obtained as
Δa1 = amean – a1,
Δa2 = amean – a2,
5. Δan = amean – an
The arithmetic mean of all the absolute errors is taken as the
mean absolute error. It is represented by Δa mean.
Δa mean = (|Δa1|+|Δa2|+|Δa3|+.....+ |Δan|)/n
Relative Error
Relative error is the ratio of the mean absolute error Δa mean
to the mean value a mean of the quantity measured.
Relative error = Δ amean /amean
Percentage Error
δa = (Δa mean /a mean) x 100%
