Scientific Notation Converter
Write any number in scientific, E and engineering notation, or turn them back.
Good to know. The Milky Way has about 10¹¹ stars. Scientific notation is how you write that without running out of zeros.
How it works
In plain words
Move the decimal point until one non-zero digit is in front of it. The number of places moved is the power of 10: positive if you moved left (a big number), negative if you moved right (a small one). Engineering notation uses only powers that are multiples of 3.
The formula
x = m × 10ⁿ, 1 ≤ |m| < 10 E notation: m e n · engineering: n a multiple of 3
Worked example
Moving the decimal point 4 places to the right turns 0.000452 into 4.52, so it is 4.52 × 10⁻⁴, or 4.52e-4 in E notation.
Sources
No outside data or rates: this is plain arithmetic.
4 automated tests check its answers on every change.
About the scientific notation converter
Scientific notation writes very large and very small numbers as a number between 1 and 10 times a power of 10. The speed of light, 300,000,000 m/s, is 3 × 10⁸; a bacterium 0.000002 m long is 2 × 10⁻⁶ m. It is called standard form in UK schools.
To convert, move the decimal point until there is one non-zero digit in front of it and count the places. Moving left, the power is positive; moving right, negative. To go back, move the point the other way by the power.
E notation is the same thing as calculators, spreadsheets and programming languages write it: 3e8 means 3 × 10⁸ and 4.52e-4 means 4.52 × 10⁻⁴. Engineering notation keeps the power a multiple of 3, which lines up with the metric prefixes: 10³ is kilo, 10⁶ mega, 10⁻³ milli and 10⁻⁶ micro. So 0.000452 A is 452 × 10⁻⁶ A, or 452 µA.
The significant figures are the digits in the number part, which show how precisely it is known. 4.52 × 10⁻⁴ has three; a trailing zero written in the number part, as in 4.520 × 10⁻⁴, is precise but is dropped here, so add it back if it matters.
Questions people ask
How do I write a number in scientific notation?
Move the decimal point so one non-zero digit is in front, and multiply by 10 to the number of places moved: 45,000 = 4.5 × 10⁴.
What does 1e6 mean?
1 × 10⁶, which is 1,000,000. The number after the e is the power of 10.
What is engineering notation?
Scientific notation with the power a multiple of 3, to match kilo, mega, milli and micro: 45,000 is 45 × 10³.