Math Tools
Convert between decimal and scientific notation instantly. See coefficient, exponent, E-notation, and engineering notation.
Scientific Notation
4.2 × 10^-4
Scientific notation is a way to express very large or very small numbers concisely. Any number is written as a × 10^b, where a (the coefficient) is between 1 and 10, and b (the exponent) is an integer. For example, 0.00042 becomes 4.2 × 10^−4. It's essential in science, medicine, and engineering.
Enter a decimal number to convert to scientific notation, or enter a coefficient and exponent to convert back to decimal form. The calculator computes the coefficient (1 ≤ a < 10) and exponent (power of 10), then displays the result in standard form, E-notation (4.2e-4), and engineering notation (4.2 × 10^−3 for multiples of 3).
Decimal to scientific: a × 10^b where a is coefficient, b is exponent | Scientific to decimal: multiply coefficient by 10^exponentTo convert decimal to scientific, find the exponent by counting how many places the decimal moves. The coefficient is the non-zero digits. To convert back, multiply the coefficient by 10 raised to the exponent power.
| Input | Result | Notes |
|---|---|---|
| 0.00042 | 4.2 × 10^−4 | Decimal point moves 4 places right, so exponent is −4; coefficient is 4.2 |
| Coefficient 6.5, Exponent 8 | 650,000,000 | 6.5 × 10^8 = 6.5 × 100,000,000 = 650,000,000 |
| 123,000,000 | 1.23 × 10^8 | Decimal point moves 8 places left, coefficient is 1.23 |
Scientific notation expresses large or small numbers compactly: 650,000,000 becomes 6.5 × 10^8. It's used in science and engineering because it's shorter, easier to compare, and reduces calculation errors.
E-notation is shorthand for scientific notation. Instead of 4.2 × 10^−4, you write 4.2e−4 or 4.2E−4. Calculators and computers often use this format because it's easier to type.
Engineering notation is scientific notation where the exponent is always a multiple of 3 (−3, 0, 3, 6, ...). This aligns with SI prefixes like milli (10^−3), kilo (10^3), mega (10^6), making it practical in engineering.
Yes. The coefficient can be any number where 1 ≤ coefficient < 10. For example, 1.0, 3.5, 9.99 are all valid. Adjust the exponent to keep it in range.
Negative numbers work the same way. For example, −0.00042 becomes −4.2 × 10^−4. The negative sign stays with the coefficient.
Yes. This is a fully client-side tool—all calculations happen in your browser. Your numbers are never sent to a server.