Error And Measurement
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General Learning Resources
Least Count:
Significant Figures:
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Non-zero digits are significant
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Zeros occurring between two non-zeros digits are significant.
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Change of units cannot change S.F.
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In the number less than one, all zeros after decimal point and to the left of first non-zero digit are insignificant
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The terminal or trailing zeros in a number without a decimal point are not significant.
Permissible Error:
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Max permissible error in a measured quantity = least count of the measuring instrument
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If nothing is given about least count then, Max permissible error = place value of the last number
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$f(x, y)=x+y$
then, $(\Delta f)_{\max }=\max \text{of} ( \pm \Delta X \pm \Delta Y)$
- f(x, y, z)=( constant )
$f(x, y, z) = x^{a} y^{b} z^{c}$
then $\left(\frac{\Delta f}{f}\right)_{\max }=\max \text{of} \left( \pm a \frac{\Delta x}{x} \pm b \frac{\Delta y}{y} \pm c \frac{\Delta z}{z}\right)$
Errors In Averaging:
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Absolute Error $\Delta a_{n}=\left|a_{\text {mean }}-a_{n}\right|$
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Mean Absolute Error $\Delta a_{\text {mean }}=\left(\sum_{i=1}^{n}\left|\Delta a_{i}\right|\right) / n$
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Relative error $ \text{Relative error} =\frac{\Delta a_{\text {mean }}}{a_{\text {mean }}}$
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Percentage error $ \text{Percentage error} =\frac{\Delta a_{\text {mean }}}{a_{\text {mean }}} \times 100$
Experiments:
- Reading of screw gauge Thickness of object = Reading of screw gauge
Least count of screw gauge = (main scale reading)+(circular scale reading)(least count)
$\text{Least count }=\frac{\text { pitch }}{\text { No. of circular scale division }}$
- Vernier callipers
Thickness of object = Reading of vernier calliper
= (main scale reading)+(vernier scale reading)(least count)
Least count of vernier calliper $\text{Least count }=1 \mathrm{MSD}-1 \mathrm{VSD}$
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