Scientific Notation Calculator
Convert between scientific and decimal notation, perform operations on numbers in scientific notation with detailed step-by-step solutions.
Scientific Notation Tool
Result
Enter values to see the conversion
Scientific Notation Rules
Standard Form
• Format: a × 10^n
• Coefficient: 1 ≤ |a| < 10
• Exponent: integer n
• Example: 3.45 × 10⁶
Large Numbers
• Move decimal left
• Positive exponent
• 1,500,000 = 1.5 × 10⁶
• 93,000,000 = 9.3 × 10⁷
Small Numbers
• Move decimal right
• Negative exponent
• 0.000123 = 1.23 × 10⁻⁴
• 0.0000056 = 5.6 × 10⁻⁶
Operations
• Multiply: add exponents
• Divide: subtract exponents
• Add/Subtract: same exponent
• Always normalize result
Examples
Example 1: Large Number Conversion
Convert 45,000,000 to scientific notation:
Move decimal 7 places left: 4.5
Result: 4.5 × 10⁷
Example 2: Small Number Conversion
Convert 0.000789 to scientific notation:
Move decimal 4 places right: 7.89
Result: 7.89 × 10⁻⁴
Example 3: Multiplication
(2.5 × 10³) × (4.0 × 10⁵)
= (2.5 × 4.0) × 10^(3+5)
= 10.0 × 10⁸ = 1.0 × 10⁹
Frequently Asked Questions
Scientific notation is a way to express very large or very small numbers as a product of a coefficient (between 1 and 10) and a power of 10. For example, 1,500,000 = 1.5 × 10⁶.
Tips
- Enter the dimensions in the same unit for consistency.
- Results update automatically as you type.
- Use the unit selector to convert between different measurement systems.