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