a) What is meant by the least count of a measuring instrument? b) Find and write the least count of this scale.

a) What is meant by the least count of a measuring instrument?

Step 1: The least count of a measuring instrument is the smallest value (length) which can be accurately measured using it.

Step 2: For a simple scale (without vernier), least count = length of the smallest division on the main scale.

b) Find and write the least count of this scale.

Step 1: Observe the given ruler scale.

The centimeter scale has major markings every $1$ cm and minor markings every $1$ mm (10 minor divisions per cm).

The inch scale has major markings every $1$ inch and minor markings every $\frac{1}{8}$ inch (or $\frac{1}{16}$ inch, but larger than $1$ mm).

Step 2: Formula for least count of simple scale:
$\text{Least count} = \text{smallest division on the scale}$

Step 3: Substitute the smallest division observed:
The smallest division is $1$ mm on the cm side.

Step 4: Simplify:
Least count = $1$ mm.

Final answer: Least count = $\boxed{1 mm}$