Scientific Notation Converter
Convert between standard notation and scientific notation (a × 10^n). Enter a very large or very small number to get it in scientific notation, or enter a coefficient and exponent to expand it to standard form.
Quick examples
How to use
- To convert to scientific notation: enter any number (big or small) and see it as a × 10^n.
- To convert from scientific notation: switch to the other mode and enter the coefficient and exponent.
- Use the quick examples to see how famous constants look in both forms.
Related tools:
Scientific notation expresses numbers as a coefficient (1 to 10) multiplied by a power of 10. The speed of light is 300,000,000 m/s - inconvenient to write or read. In scientific notation: 3.0 x 10^8 m/s. A hydrogen atom radius is 0.0000000529 nm, or 5.29 x 10^-11 m. Both extremes become manageable.
Multiplication and division in scientific notation are elegant: multiply the coefficients and add (or subtract) the exponents. (3 x 10^8) x (2 x 10^5) = 6 x 10^13. This is why scientists prefer it - arithmetic with very large and small numbers becomes straightforward without counting zeros.
Frequently Asked Questions
How do I convert a number to scientific notation?
Move the decimal point until only one non-zero digit is to the left of it. Count the moves - that is your exponent. Moving left means positive exponent (large number); moving right means negative exponent (small number). 45,000 = 4.5 x 10^4. 0.0045 = 4.5 x 10^-3.
What is E notation on a calculator?
E notation is shorthand for scientific notation: 4.5E4 means 4.5 x 10^4. You will see this in spreadsheets and programming languages. It is the same thing, just written without the explicit 10^ symbol.
When is scientific notation required vs optional?
In scientific fields, it is often required in published work for clarity. In everyday use, it is optional but helpful whenever a number has more than about 6-7 digits. A tax bill in rupees does not need it; a national GDP in rupees probably does.