What is Scientific Notation?
N = a × 10ⁿ where 1 ≤ |a| < 10
Examples: 6,500,000 = 6.5 × 10⁶ 0.00034 = 3.4 × 10⁻⁴
Examples: 6,500,000 = 6.5 × 10⁶ 0.00034 = 3.4 × 10⁻⁴
Scientific Notation Rules
| Operation | Rule | Example |
|---|---|---|
| Multiply | Multiply coefficients, add exponents | (3×10²)×(4×10³) = 12×10⁵ = 1.2×10⁶ |
| Divide | Divide coefficients, subtract exponents | (6×10⁵)÷(2×10²) = 3×10³ |
| Add/Subtract | Match exponents first, then add/subtract | 3×10⁴ + 2×10³ = 3.2×10⁴ |
Common Scientific Notation Values
| Value | Scientific Notation | Context |
|---|---|---|
| Speed of light | 3×10⁸ m/s | Physics |
| Avogadro number | 6.022×10²³ | Chemistry |
| 1 nanometer | 1×10⁻⁹ m | Nanotechnology |
| Earth's mass | 5.972×10²⁴ kg | Astronomy |
| Electron charge | 1.602×10⁻¹⁹ C | Physics |
| US national debt | ~3.5×10¹³ dollars | Economics |
Frequently Asked Questions
What is E notation?
E notation (used on calculators and in programming) writes "×10ⁿ" as "En". So 6.5E6 means 6.5×10⁶. Python, JavaScript, and most calculators use this format. This calculator accepts both formats as input.
How do I convert a decimal to scientific notation?
Move the decimal point until one non-zero digit is to its left. Count the moves — moves right give a negative exponent; moves left give a positive exponent. Example: 0.00045 → move 4 places right → 4.5×10⁻⁴.
Why is scientific notation used?
Scientific notation makes it practical to write and compute with very large or very small numbers. Comparing 5,980,000,000,000,000,000,000,000 kg and 6×10²⁴ kg is much easier with notation. It also clearly shows the number of significant figures.