Formula
Scientific notation format
Normalized form N = a × 10ⁿ, where 1 ≤ |a| < 10
The coefficient a carries the significant digits and the integer exponent n shows how many powers of ten scale the value. Negative values keep a negative coefficient.
Worked example
Worked decimal conversion example
Convert 0.000456 to scientific notation.
- Move the decimal four places right to obtain 4.56.
- Moving right produces a negative exponent.
- Write the result as 4.56 × 10⁻⁴.
Calculation guidance
Operating with powers of ten
- For multiplication, multiply coefficients and add exponents.
- For division, divide coefficients and subtract exponents.
- For addition or subtraction, first express both values with a common exponent.
- Normalize the coefficient after completing the operation.
Assumptions and limitations
Precision and numeric limits
- Results use JavaScript double-precision arithmetic.
- Extremely large or small values outside the supported numeric range are rejected.
- The exponent must be a whole number.
- Displayed coefficients support between 1 and 12 significant figures.
- Precision selection should reflect the uncertainty of measured inputs.
Questions and answers
Scientific notation FAQ
What is normalized scientific notation?
Normalized scientific notation writes a number as a coefficient with an absolute value from 1 up to, but not including, 10 multiplied by a power of ten.
How do I convert a decimal to scientific notation?
Move the decimal point until one nonzero digit remains to its left. The number of places moved becomes the exponent; moving left gives a positive exponent and moving right gives a negative exponent.
How do significant figures affect the result?
The selected precision rounds the displayed coefficient. Choose a precision that reflects the least precise measured input rather than adding unsupported certainty.