Scientific Notation Calculator
Convert numbers to scientific, E and engineering notation, count significant figures, and add, subtract, multiply or divide with sig fig rounding.
The interactive tool loads here when JavaScript runs.
About this toolWhat is the Scientific Notation Calculator?
Paste a number in any common form, such as 0.000047, 4.7e-5 or 4.7 × 10^-5, and see it in scientific notation, E notation, engineering notation with its SI prefix, and as a plain decimal. The page counts the significant figures you typed and can round to any number of them.
Switch to Calculate to add, subtract, multiply or divide two numbers in scientific notation. You get the exact result and the result rounded by the significant-figure rules used in chemistry and physics classes, with the rule that was applied written out.
Numbers are handled as exact decimals rather than binary floating point, so 6.02214076 × 10²³ converts to a 24-digit integer without stray digits and trailing zeros you typed are kept as significant.
- Scientific, E, engineering and plain decimal forms
- SI prefix for engineering notation, from quecto to quetta
- Significant figure counting with ambiguity warnings
- Arithmetic with sig fig rounding and the rule shown
- Exact decimal arithmetic without floating-point errors
How to use the Scientific Notation Calculator
- Choose Convert to change the form of one number, or Calculate for arithmetic.
- Type the number as a decimal, in E notation (3.0e8), or as 3.0 × 10^8. Spaces and commas are ignored.
- In Convert, optionally pick how many significant figures to round to.
- In Calculate, enter two numbers and pick +, −, × or ÷.
- Read the scientific, E, engineering and decimal forms, plus the significant-figure rule used, then copy the result.
Worked examples
A small number
Input
0.000047
Output
4.7 × 10⁻⁵; 4.7e-5; 47 × 10⁻⁶ (micro)
The point moves five places right to give 4.7, so the exponent is −5. Engineering notation uses −6, the micro prefix.
Rounding a constant
Input
299792458 to 3 significant figures
Output
3.00 × 10⁸
The fourth digit is 7, so 2.99 rounds up and carries to 3.00. The two zeros are kept because they are significant.
Multiplying
Input
3.0e8 × 2.50e-3
Output
7.5 × 10⁵ (2 s.f.)
Coefficients multiply to 7.5 and exponents add to 5. 3.0 has two significant figures, so the answer keeps two.
Adding
Input
12.11 + 18.0
Output
30.1
The exact sum is 30.11, but 18.0 is only known to tenths, so the result is rounded to tenths.
Background and insight
Scientific notation writes a number as m × 10ⁿ with 1 ≤ |m| < 10. The exponent counts how far the decimal point moved: left for large numbers (positive n), right for small ones (negative n). E notation is the same thing written for keyboards, 4.7e-5, and is how calculators, spreadsheets and programming languages print it. Engineering notation restricts n to multiples of 3 so the exponent lines up with SI prefixes: 47 × 10⁻⁶ is 47 micro.
Significant figures record how precisely a value is known. Non-zero digits always count; zeros between them count; leading zeros never count; trailing zeros count when there is a decimal point. A whole number like 1200 is ambiguous: it could have two, three or four significant figures, which is one reason scientists write 1.20 × 10³ instead. The calculator treats 1200 as two and tells you about the ambiguity.
Results inherit precision from their inputs. For multiplication and division, keep as many significant figures as the least precise input. For addition and subtraction, round to the decimal place of the least precise input. Defined constants are exact: since 2019 the SI fixes Avogadro's number at 6.02214076 × 10²³ and the elementary charge at 1.602176634 × 10⁻¹⁹ C, and the speed of light has been exactly 299,792,458 m/s since 1983.
Common use cases
Chemistry and physics
Convert moles, charges and wavelengths, and round lab results to the right number of significant figures.
Electronics
Read 4.7e-6 F as 4.7 µF or 0.000047 A as 47 µA with the engineering form and SI prefix.
Data and code
Make sense of E notation from spreadsheets, JSON or log files, and convert back to full decimals.
Astronomy and big numbers
Write distances and masses compactly and multiply or divide them without losing track of zeros.
Tips and limitations
- Type a decimal point after a whole number (1200.) or use E notation (1.200e3) to mark trailing zeros as significant.
- Round only at the end of a multi-step calculation; rounding each step can shift the last digit.
- Exact counts (12 eggs) and defined constants have unlimited significant figures and never limit a result.
- In spreadsheets, a long ID that turns into 1.23E+15 has already lost digits; format the column as text before pasting.
- Division results are exact to 40 digits before rounding, which is far beyond any measured quantity.
Frequently asked questions
How do you convert a number to scientific notation?
Move the decimal point until exactly one non-zero digit is left of it, and count the moves. Moving left gives a positive exponent, moving right a negative one. 123,456 becomes 1.23456 × 10⁵; 0.00042 becomes 4.2 × 10⁻⁴.
What is E notation?
E notation writes × 10^n as e or E followed by n, so 4.2 × 10⁻⁴ is 4.2e-4 or 4.2E-04. It is used by calculators, spreadsheets and programming languages that cannot show superscripts.
What is the difference between scientific and engineering notation?
Scientific notation keeps one digit before the point (4.7 × 10⁻⁵). Engineering notation uses exponents that are multiples of 3 and allows 1 to 3 digits before the point (47 × 10⁻⁶), matching SI prefixes like kilo, mega, milli and micro.
How many significant figures does a number have?
Count from the first non-zero digit. Include zeros between digits and trailing zeros after a decimal point. 0.00420 has 3, 100.05 has 5, and 1200 has 2 unless a decimal point (1200.) shows the zeros are measured.
How do you multiply numbers in scientific notation?
Multiply the coefficients and add the exponents, then adjust so the coefficient is between 1 and 10. (3.0 × 10⁸) × (2.50 × 10⁻³) = 7.5 × 10⁵. Round to the fewest significant figures among the inputs.
How do you add numbers in scientific notation?
Rewrite them with the same power of ten, add the coefficients, then normalise. 3.2 × 10⁴ + 5 × 10³ = 3.2 × 10⁴ + 0.5 × 10⁴ = 3.7 × 10⁴.
Is there an in-depth guide to the Scientific Notation Calculator?
Yes. “Quadratics, Scientific Notation and Roman Numerals: Writing Numbers Well” covers the background, how it works, common pitfalls and worked examples. Read the full guide.
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