Scientific Notation Calculator
Scientific notation is a way of writing numbers that are too large or too small to be written conveniently in standard decimal form. It expresses every number as a coefficient multiplied by a power of ten, where the coefficient is always a value between 1 and 10. For example, the number 0.000045 becomes 4.5 times 10 to the power of negative 5, which is far more compact and easier to use in calculations. Scientists, engineers, and students rely on this notation daily because it allows accurate comparison and arithmetic across values that might otherwise span dozens of digits. This calculator converts any number you enter into scientific notation instantly, and also accepts a coefficient and exponent to convert back to standard decimal form. You enter your number in the first input field, and the calculator returns the coefficient and exponent separately, the full scientific notation expression, the order of magnitude, and the equivalent engineering notation where the exponent is always a multiple of three to match standard metric prefixes such as milli, kilo, and mega. The tool handles very large numbers such as the speed of light and very small ones such as the wavelength of light equally well, and works with both positive and negative inputs. For the reverse conversion, enter a coefficient and an exponent and the calculator expands them into the standard decimal number. It is useful for physics and chemistry students, electronics engineers, and anyone needing to express measurements or constants in a compact, standardised form. Results are exact to the precision of the input you provide.
How it works
To convert a number to scientific notation, the calculator finds the base-10 logarithm of the absolute value and floors it to get the exponent. The coefficient is the original number divided by 10 raised to that exponent, which always produces a value between 1 and 10 (or between -10 and -1 for negative inputs). The order of magnitude is that same floored exponent. For engineering notation, the exponent is rounded down to the nearest multiple of three and the coefficient is recalculated accordingly. To convert back from scientific notation to standard decimal form, multiply the coefficient by 10 raised to the exponent.
Worked example
Enter 0.000045 in the number field. The base-10 logarithm of 0.000045 is approximately -4.35, which floors to -5. Dividing 0.000045 by 10 to the power of -5 gives a coefficient of 4.5. The scientific notation result is 4.5 x 10^-5. The order of magnitude is -5. For engineering notation, the nearest multiple of three at or below -5 is -6, so the result adjusts to 45 x 10^-6, equivalent to 45 microunits in SI notation.
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