Expanded Form Calculator
Convert numbers to expanded form showing place value with numbers, factors, or exponents
Convert Number to Expanded Form
Enter any positive or negative number with or without decimals
Choose how to display the expanded form
Example Calculations
Example 1: Integer
Number: 3,547
Numbers Form: 3000 + 500 + 40 + 7
Factors Form: 3×1000 + 5×100 + 4×10 + 7×1
Exponents Form: 3×10³ + 5×10² + 4×10¹ + 7×10⁰
Example 2: Decimal
Number: 25.306
Numbers Form: 20 + 5 + 0.3 + 0.006
Factors Form: 2×10 + 5×1 + 3×0.1 + 6×0.001
Exponents Form: 2×10¹ + 5×10⁰ + 3×10⁻¹ + 6×10⁻³
Example 3: Negative Number
Number: -184.05
Numbers Form: -100 + 80 + 4 + 0.05
Factors Form: -1×100 + 8×10 + 4×1 + 5×0.01
Exponents Form: -1×10² + 8×10¹ + 4×10⁰ + 5×10⁻²
Example 4: Large Number
Number: 1,234,567
Exponents Form:
1×10⁶ + 2×10⁵ + 3×10⁴ + 4×10³ + 5×10² + 6×10¹ + 7×10⁰
Place Value Chart
Form Types
Numbers Form
Shows actual place values
700 + 30 + 5
Factors Form
Shows digit × place value
7×100 + 3×10 + 5×1
Exponents Form
Uses powers of 10
7×10² + 3×10¹ + 5×10⁰
Quick Tips
Zero digits are omitted in expanded form
Each digit represents a power of 10
Decimal places use negative powers
Expanded form helps understand place value
Understanding Expanded Form
What is Expanded Form?
Expanded form is a way to write numbers that shows the value of each digit based on its position in the number. Each digit is broken down into its place value components and written as a sum.
Why is it Important?
- •Helps understand place value concept
- •Foundation for arithmetic operations
- •Connects to scientific notation
- •Essential for mathematical understanding
Powers of 10
10³ = 1,000 (thousands)
10² = 100 (hundreds)
10¹ = 10 (tens)
10⁰ = 1 (ones)
10⁻¹ = 0.1 (tenths)
10⁻² = 0.01 (hundredths)
10⁻³ = 0.001 (thousandths)
Remember: Any number to the power of 0 equals 1, and negative powers create decimal values.
Educational Benefits
- • Visual representation of numbers
- • Place value understanding
- • Preparation for algebra
- • Number sense development
Real-World Applications
- • Scientific notation
- • Computer science (binary expansion)
- • Engineering calculations
- • Financial modeling
Mathematical Connections
- • Polynomial representation
- • Logarithms and exponents
- • Decimal system understanding
- • Number base conversions