Scientific Notation Converter
Convert a number to and from scientific notation.
Enter any number to see it in scientific notation (like 4.2 × 10⁻⁴) and standard form. Handy for very large or very small numbers in science and engineering.
Formula / method
Examples
4.2 × 10^-4
9.3 × 10^7
What scientific notation is
Scientific notation writes any number as a coefficient multiplied by a power of ten, in the form m x 10^n, where the coefficient m is at least 1 and less than 10. For example 6.022 x 10^23 and 1.6 x 10^-19 are far easier to read and compare than the same values written out with dozens of zeros. This converter turns an ordinary number into that compact form and expands scientific notation back into a plain decimal.
A positive exponent shifts the decimal point to the right and represents a large number, while a negative exponent shifts it left and represents a small fraction.
Where it helps
Scientists, engineers and students rely on this notation to keep track of magnitude when values span from the size of an atom to the distance between stars. It also makes multiplication and division simpler, because you can add or subtract the exponents separately from the coefficients.
A common slip is forgetting the normalisation rule: 42 x 10^3 is valid arithmetic but is not standard scientific notation, since the coefficient must sit between 1 and 10. Written correctly it becomes 4.2 x 10^4. Some fields prefer engineering notation, where the exponent is always a multiple of three.
Where it's used
- Writing a very large or very small number compactly, like Avogadro's number
- Entering values into a scientific calculator or spreadsheet
- Reading distances in astronomy or particle sizes in chemistry and physics
- Comparing two quantities by their order of magnitude
- Turning a long decimal like 0.00000042 into 4.2 × 10⁻⁷
Real-world examples
- 0.00042 converts to 4.2 × 10⁻⁴.
- The 93,000,000-mile distance to the Sun is written 9.3 × 10⁷.
- Avogadro's number, 602,214,076,000,000,000,000,000, compresses to about 6.022 × 10²³.
Did you know?
The idea of a compact system for enormous numbers goes back to Archimedes' essay The Sand Reckoner (about 250 BC), in which he built up powers of numbers to estimate how many grains of sand would fill the entire universe — reaching a figure on the order of 10⁶³.
FAQ
What is scientific notation for?
It makes very large or very small numbers compact and easy to compare — for example, 9.3 × 10⁷ instead of 93,000,000.