1. Find the value of one main scale division (MSD)

Each $1\,\text{cm}$ on the main scale is divided into $20$ equal parts.

$1\,\text{MSD} = \frac{1\,\text{cm}}{20} = \frac{10\,\text{mm}}{20} = 0.5\,\text{mm}$

2. Use the coincidence condition

Given: the 10th vernier scale division coincides with the 9th main scale division.

So,

$10\,\text{VSD} = 9\,\text{MSD}$

Therefore,

$1\,\text{VSD} = \frac{9}{10}\,\text{MSD}$

3. Find the vernier constant (least count)

For a direct vernier,

$\text{Vernier Constant} = 1\,\text{MSD} - 1\,\text{VSD}$

Substitute $1\,\text{VSD} = \frac{9}{10}\,\text{MSD}$:

$\text{VC} = 1\,\text{MSD} - \frac{9}{10}\,\text{MSD} = \frac{1}{10}\,\text{MSD}$

Now, since

$1\,\text{MSD} = 0.5\,\text{mm}$

we get

$\text{VC} = \frac{1}{10} \times 0.5 = 0.05\,\text{mm}$

4. Match with the required format

We need

$0.05\,\text{mm} = 5 \times 10^{-2}\,\text{mm}$

So the blank is:

$\boxed{5}$

5. Comparison with stored correct answer

Stored correct answer = $5$

Derived answer = $5$

They match.