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Scientific notation writes any number as a coefficient between 1 and 10 times a power of ten — 1.5 × 10³ instead of 1500, or 4.2 × 10⁻⁴ instead of 0.00042. It's how scientists and engineers keep very large and very small numbers readable and their precision clear.
Convert a plain decimal into scientific notation, or expand scientific notation back into a decimal.
How is it calculated?
The two directions
Decimal → scientific notation. Move the decimal point until one non-zero digit remains to its left; the number of places you moved is the exponent. Move left and the exponent is positive; move right and it's negative.
| Number | Scientific notation |
|---|---|
| 1500 | 1.5 × 10³ |
| 384,400 | 3.844 × 10⁵ |
| 0.00042 | 4.2 × 10⁻⁴ |
| 0.0000000091 | 9.1 × 10⁻⁹ |
Scientific → decimal. A positive exponent shifts the point right (bigger); a negative one shifts it left (smaller). 6.022 × 10²³ becomes 602,200,000,000,000,000,000,000.
E-notation
Calculators and code write "× 10ⁿ" as the letter E: 1.5 × 10³ is `1.5e3`, and 4.2 × 10⁻⁴ is `4.2e-4`. The tool accepts either form on input and shows the E-notation alongside the result, so you can paste values straight into a spreadsheet or program.
Why the coefficient must be 1–10
Keeping exactly one non-zero digit before the decimal point (normalised form) makes numbers directly comparable by their exponent and unambiguous to read. 15 × 10² and 1.5 × 10³ are equal, but only the second is proper scientific notation.
Where it helps
Physics and chemistry constants, astronomical distances, molecular scales, and any figure with a long run of zeros. It also makes multiplying and dividing such numbers easy: multiply the coefficients and add the exponents.
Worked example
Convert 1500 to scientific notation: move the decimal point three places left to sit after the 1, giving 1.5 × 10³ (E-notation 1.5e3), coefficient 1.5 and exponent 3. Going the other way, 4.2e-4 means moving the point four places left from 4.2, which expands to 0.00042. The exponent is negative because the original number is smaller than 1.
FAQ
What is scientific notation?+
It expresses a number as a coefficient between 1 and 10 multiplied by a power of ten, such as 1.5 × 10³. It keeps very large or very small numbers compact and their precision explicit.
How do I convert a number to scientific notation?+
Move the decimal point until one non-zero digit is to its left; the number of places moved is the exponent, positive if you moved left, negative if right. 0.00042 becomes 4.2 × 10⁻⁴.
What is E-notation?+
It is how calculators and code write "× 10ⁿ" using the letter E: 1.5e3 means 1.5 × 10³ and 4.2e-4 means 4.2 × 10⁻⁴. This tool reads and displays both forms.
Why must the coefficient be between 1 and 10?+
Normalising to exactly one non-zero digit before the point makes numbers comparable by exponent and unambiguous. 15 × 10² is not proper form; 1.5 × 10³ is.
What does a negative exponent mean?+
A negative exponent marks a number smaller than 1: 10⁻³ is one thousandth. So 4.2 × 10⁻⁴ equals 0.00042, with the decimal point shifted four places left.