Convert to and from scientific notation. This free converter turns ordinary numbers into a × 10ⁿ form (and back), and also shows engineering and E-notation.
Enter an ordinary number to convert it into scientific notation (a × 10ⁿ, with 1 ≤ |a| < 10), plus engineering and E-notation forms.
Enter the coefficient and exponent of a × 10ⁿ to convert it back to an ordinary decimal number.
Scientific notation writes a number as a coefficient between 1 and 10 times a power of ten. Engineering notation uses exponents that are multiples of 3 (matching SI prefixes like kilo, mega, milli).
How the Scientific Notation Converter Works
Scientific notation rewrites a number as a small coefficient multiplied by a power of ten, which makes very large or very small numbers easier to read and compare. This tool converts either direction: type an ordinary decimal to get its scientific, engineering, and E-notation forms, or enter a coefficient and exponent to get the plain decimal back.
Formula: For a number x, the exponent is n = floor(logâ‚â‚€(|x|)), and the coefficient is a = x ÷ 10^n, adjusted so that 1 ≤ |a| < 10. The result is written as a × 10^n. Engineering notation uses the same coefficient idea but forces the exponent down to the nearest multiple of 3 (so a can range from 1 up to just under 1000). To convert back, plain decimal = a × 10^n.
- Decimal number — the ordinary number you want converted into scientific notation (used in “From decimal” mode)
- Coefficient (a) — the leading number in a × 10^n, entered in “From scientific” mode to convert back to decimal
- Exponent (n) — the power of ten paired with the coefficient, entered in “From scientific” mode
Example Scenarios
| Decimal Number | Scientific Notation | Engineering Notation |
|---|---|---|
| 92,500,000 | 9.25 × 10^7 | 92.5 × 10^6 |
| 0.00045 | 4.5 × 10^-4 | 450 × 10^-6 |
| 1,500 | 1.5 × 10^3 | 1.5 × 10^3 |
| 0.5 | 5 × 10^-1 | 500 × 10^-3 |
| 123,456 | 1.23456 × 10^5 | 123.456 × 10^3 |
Scientific Notation Converter FAQ
Why must the coefficient always be between 1 and 10?
By convention, scientific notation is only considered “normalized” when the coefficient a satisfies 1 ≤ |a| < 10. This keeps the format consistent so any two numbers in scientific notation can be compared just by looking at their exponents first.How is engineering notation different from scientific notation?
Engineering notation uses the same a × 10^n idea, but restricts the exponent to multiples of 3 (…, -6, -3, 0, 3, 6…). This lines up with SI unit prefixes like kilo, mega, and milli, so the coefficient can be anywhere from 1 up to just under 1000 instead of strictly under 10.What does E-notation mean, like the “1.23e5” some calculators show?
E-notation is a plain-text way of writing scientific notation without a multiplication sign or superscript exponent. “1.23e5” means 1.23 × 10^5. Spreadsheets and calculators use it because typing a caret or superscript is awkward in a single text field.How do I convert scientific notation back into an ordinary number?
Switch to “From scientific” mode, enter the coefficient in the coefficient field and the exponent in the exponent field, then multiply them out: decimal = coefficient × 10^exponent. The converter displays the expanded plain-decimal result automatically.Can this converter handle negative numbers and negative exponents?
Yes. A negative decimal number keeps its sign in the coefficient (for example -0.00045 becomes -4.5 × 10^-4), and a negative exponent simply means the original number was smaller than 1, such as a fraction or a very small decimal.Why do very small decimals end up with a negative exponent?
The exponent n is found from floor(logâ‚â‚€(|x|)). For numbers smaller than 1, logâ‚â‚€ of the value is negative, so n comes out negative too — that’s how the converter signals “divide by a power of ten” rather than “multiply.”Related Calculators
Working with very large or very small numbers often means juggling precision as well as notation — the significant figures calculator helps you decide how many digits to keep, the exponent calculator handles raising numbers to a power, and the full scientific calculator covers everything else in between.