Scientific notation converter
Type a very large or very small number, in normal form or something like 6.02e23, choose how many significant figures to keep and see it in every common notation.
How this calculator works
Scientific notation (called standard form in the UK) writes a number as something between 1 and 10 multiplied by a power of ten. It keeps huge and tiny numbers readable: the mass of an electron is easier to say as 9.11 × 10⁻³¹ kg than as a decimal with thirty zeros.
The power of ten counts how far the decimal point moved. Move it left and the power is positive, move it right and the power is negative. The calculator shows that move in words, rounds to the number of significant figures you ask for, and also gives engineering notation, where the power is always a multiple of three so it lines up with prefixes like kilo, mega and milli.
The formula behind it
- N = a × 10ⁿ with 1 ≤ a < 10 and n a whole number
- Engineering: same idea, but n is a multiple of 3 and a can be up to 999
- E-notation: 4.52E-4 means 4.52 × 10⁻⁴
A worked example
0.000452 needs the decimal point moved 4 places to the right to give 4.52, so it is 4.52 × 10⁻⁴. In engineering notation that is 452 × 10⁻⁶, i.e. 452 micro-units.
Questions people ask
What are significant figures?
The digits that carry real information, counted from the first non-zero digit. 0.000452 has three. Rounding to fewer keeps the leading digits and drops the rest.
How do I type scientific notation into a calculator?
Use the EXP or EE key. To enter 3.2 × 10⁸ press 3.2, EXP, 8. Do not type ×10 as well, or the answer will be a factor of ten out.
Can the number be negative?
Yes. The sign stays with the front part, so -0.5 becomes -5.00 × 10⁻¹.
Why does 10 × 10³ not count as standard form?
Because the front number must be less than 10. Written correctly it is 1 × 10⁴.