How to Use Scientific Notation
Scientific notation is a way of expressing very large or very small numbers in a compact, standardized form. It's essential in physics, chemistry, astronomy, and engineering where numbers like the mass of an electron (0.000000000000000000000000000000911 kg) or the distance to a galaxy (93,000,000,000,000,000,000,000 km) would be impractical to write out.
The Form
N × 10ˣ
Where N is a number between 1 and 10 (1 ≤ N < 10), and x is an integer exponent.
Converting to Scientific Notation
Large numbers: Move the decimal point left until you have a number between 1 and 10. Count the moves—that's your positive exponent.
Example: 4,500,000 = 4.5 × 10⁶ (moved 6 places left)
Small numbers: Move the decimal point right until you have a number between 1 and 10. Count the moves—that's your negative exponent.
Example: 0.0000032 = 3.2 × 10⁻⁶ (moved 6 places right)
Multiplying in Scientific Notation
(a × 10ᵐ) × (b × 10ⁿ) = (a × b) × 10^(m+n)
Example: (3 × 10⁴) × (2 × 10³) = 6 × 10⁷
Dividing in Scientific Notation
(a × 10ᵐ) ÷ (b × 10ⁿ) = (a/b) × 10^(m−n)
Example: (8 × 10⁶) ÷ (4 × 10²) = 2 × 10⁴
Common Scientific Notation Values
| Standard Notation | Scientific Notation |
|---|---|
| 1,000 | 1 × 10³ |
| 1,000,000 | 1 × 10⁶ |
| 0.001 | 1 × 10⁻³ |
| Speed of light | 3 × 10⁸ m/s |
| Mass of proton | 1.67 × 10⁻²⁷ kg |
Use our scientific notation calculator for any conversion.