Least Count:

Significant Figures:

• Non-zero digits are significant

• Zeros occurring between two non-zeros digits are significant.

• Change of units cannot change S.F.

• In the number less than one, all zeros after decimal point and to the left of first non-zero digit are insignificant

• The terminal or trailing zeros in a number without a decimal point are not significant.

Permissible Error:

• Max permissible error in a measured quantity = least count of the measuring instrument

• If nothing is given about least count then, Max permissible error = place value of the last number

• $$f(x, y)=x+y$$

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:

• Absolute Error $$\Delta a_{n}=\left|a_{\text {mean }}-a_{n}\right|$$

• Mean Absolute Error $$\Delta a_{\text {mean }}=\left(\sum_{i=1}^{n}\left|\Delta a_{i}\right|\right) / n$$

• Relative error $$ \text{Relative error} =\frac{\Delta a_{\text {mean }}}{a_{\text {mean }}}$$

• 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 $$\text{Least count }=1 \mathrm{MSD}-1 \mathrm{VSD}$$