### Theory:

Procedure to expand the number using exponential:
Step 1: Identify the place value of each digit and write it in additional form.

Step 2: Multiply each digit by its place value.

Step 3: Mention the place values in power of $$10$$'s.
Example:
1. Write the expanded form of $$3854$$ using exponential.

$$3854$$ $$=$$ $$3000 + 800 + 50 + 4$$

$$=$$ $$(3 \times 1000) + (8 \times 100) + (5 \times 10) + (4 \times 1)$$

$$=$$ $$(3 \times 10^3) + (8 \times 10^2) + (5 \times 10^1) + (4 \times 10^0)$$

The expanded form of $$3854$$ $$=$$ $$(3 \times 10^3) + (8 \times 10^2) + (5 \times 10^1) + (4 \times 10^0)$$.

2. Write the expanded form of $$438.54$$ using exponential.

$$438.54$$ $$=$$ $$400 + 30 + 8 + \frac{5}{10}+ \frac{4}{100}$$

$$=$$ $$(4 \times 100) + (3 \times 10) + (8 \times 1) + (5 \times \frac{1}{10}) + (4 \times \frac{1}{100})$$

$$=$$ $$(4 \times 10^2) + (3 \times 10^1) + (8 \times 10^0) + (5 \times 10^{-1}) + (4 \times 10^{-2})$$

The expanded form of $$438.54$$ $$=$$ $$(4 \times 10^2) + (3 \times 10^1) + (8 \times 10^0) + (5 \times 10^{-1}) + (4 \times 10^{-2})$$.