Units and Measurements Part 1

According to the question,
One division of main scale reading = a cm
nth vernier scale division=(n−1) th main scale division
∴ One division of vernier scale reading =‌

(n−1)×a

n

...(i)
We know that,
Least count (LC)=
[1 main scale division −1 vernier scale division] cm
=a−‌

(n−1)a

n

  [using Eq. (i)]
=‌

a(n−n+1)

n

=‌

a

n

cm=‌

a

n

×10mm
⇒‌‌LC=‌

10a

n

mm