Scientific Notation Calculator

Scientific notation is a way to express very large or very small numbers in a compact form. It's widely used in science, engineering, and mathematics to handle numbers that would be impractical to write in standard decimal form.

Format

• Standard Form: a × 10^n
• Coefficient (a): 1 ≤ |a| < 10
• Exponent (n): Integer (positive or negative)
• Base: Always 10

Types of Notation

• Scientific: 1.23 × 10^6 (coefficient between 1-10)
• Engineering: 123 × 10^4 (exponent is multiple of 3)
• E-notation: 1.23e6 (computer/calculator format)

Examples

• Distance to sun: 1.5 × 10^8 km
• Mass of electron: 9.11 × 10^-31 kg
• Speed of light: 3 × 10^8 m/s
• Size of atom: ~10^-10 meters

Operations

• Multiplication: (a × 10^m) × (b × 10^n) = (a × b) × 10^(m+n)
• Division: (a × 10^m) ÷ (b × 10^n) = (a ÷ b) × 10^(m-n)
• Addition/Subtraction: Convert to same exponent first

Applications

• Astronomy: Distances and masses in space
• Physics: Atomic and subatomic measurements
• Chemistry: Molecular quantities and concentrations
• Biology: Cell sizes and population counts
• Engineering: Precision measurements and calculations