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Convert between decimal and scientific notation instantly. See coefficient, exponent, E-notation, and engineering notation.
Scientific Notation
4.2 × 10^-4
The Scientific Notation Calculator converts numbers between decimal and scientific notation in seconds. Whether you're working on physics homework, engineering calculations, or analyzing very large and very small numbers, this tool gives you precise scientific, E-notation, and engineering notation results.
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.