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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.
Scientific Notation Calculator: step-by-step worked example
Write the speed of light (299,792,458 m/s) in scientific notation.
- Direction
- Decimal → scientific notation
- Value
- 299792458
- 1
Find the exponent
n = ⌊log₁₀ |x|⌋ (how many places the point moves)
⌊log₁₀ 299,792,458⌋ = ⌊8.4768⌋ = 8
- 2
Find the coefficient
a = x ÷ 10ⁿ (1 ≤ |a| < 10)
299,792,458 ÷ 10⁸ = 2.99792458
- 3
Scientific notation
x = a × 10ⁿ
2.99792458 × 10⁸ = 2.99792458 × 10^8
- 4
E notation (calculators / Excel)
a e n
= 2.99792458e8
Good to know: The coefficient must be at least 1 and less than 10: 29.98 × 10⁷ is not normalized. Numbers below 1 get a negative exponent (0.00042 = 4.2 × 10⁻⁴).
Scientific Notation Calculator — how it works
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.
Frequently asked questions
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.
About this page
- Publisher:
- Kalkoro — Teknolojig Bilişim Teknolojileri A.Ş., İstanbul
- Written by:
- Ahmet Tur — Editor (Math, date & time, unit conversion, physics & chemistry, everyday tools)
- Reviewed by:
- Kübra Yıldız — Editor
Parameters come from official sources; the last update date is shown at the bottom of the page.
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