Least count (LC) = Length of one main scale division - Length of one vernier scale division

$\Rightarrow$ LC = 1 MSD - 1 VSD

Vernier scale reading (VSR): If n^th division of Vernier scale coincides with some division on main scale, then Vernier scale reading is n × LC.

Total reading = MSR + VSR

$\Rightarrow$Total reading = MSR + n × Least Count

Pitch of the screw $=\frac{\text{ Distance moved by screwed rod }}{\text{ Number of rotations }}$

Least Count = $=\frac{\text{ Pitch }}{\text{ Total number of divisions on circular scale }}$

When n^th division of circular scale is aligned with reference line then circular scale reading is n multiplied with least count (CSR = n $\times$ LC).

Linear scale reading and circular scale reading are added to get the total reading.

$\therefore$ Total reading = LSR + CSR

$\Rightarrow$ Total Reading = LSR + n × LC.

Angle $=\frac{\text { arc }}{\text { radius }}$

or $\theta=\frac{a}{D}$,

Here $a$ is the length of arc and $D$ is the radius.

$1 \mathrm{AU}=1.496 \times 10^{11} \mathrm{~m}$

1 Light year $=9.46 \times 10^{15} \mathrm{~m}$

Let $x_1, x_2, x_3 \ldots \ldots x_n$ be the measured values of a given physical quantity $x$ then

1. $x_{\text {mean }}=\frac{x_1+x_2+\cdots+x_n}{n}$

$$ x_{\text {mean }}=\frac{\sum_{i=1}^{i=n} x_i}{n} $$

2. Mean absolute error,

$$ \Delta x_{\text {mean }}=\frac{\left|\Delta x_1\right|+\left|\Delta x_2\right|+\cdots+\left|\Delta x_n\right|}{n} $$

$$ =\frac{\sum_{i=1}^{i=n}\left|\Delta x_i\right|}{n} $$

where $\left|\Delta x_1\right|=\left|x_1-x_{\text {mean }}\right|$,

$\left|\Delta x_2\right|=\left|x_2-x_{\text {mean }}\right|$ and so on.

3. Fractional error/Relative error

$$ =\frac{\Delta x_{\text {mean }}}{x_{\text {mean }}} $$

4. Percentage error

$$ =\frac{\Delta x_{\text {mean }}}{x_{\text {mean }}} \times 100 $$