Scientific notation converter
Enter any number and read it back in every notation, without a float ever touching it.
Mantissa
4.5678
- Power of ten
- -5
- Engineering mantissa
- 45.678
- Engineering exponent Always a multiple of three.
- -6
- The number itself
- 0.000 045 678
Show the working
- Number = 0.000 045 678
- Power of ten = 0.000 045 678 != 0 ? floor(log10(abs(0.000 045 678))) : 0 = -5
- Mantissa = 0.000 045 678 != 0 ? 0.000 045 678 / 10^-5 : 0 = 4.5678
- Engineering exponent = floor(-5 / 3) * 3 = -6
- Engineering mantissa = 0.000 045 678 != 0 ? 0.000 045 678 / 10^-6 : 0 = 45.678
- The number itself = 0.000 045 678 = 0.000 045 678
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- x = m x 10^e with 1 <= |m| < 10
- Engineering notation forces e to a multiple of three.
The exponent is derived from an exact integer base-10 logarithm, so it is right even for numbers with hundreds of digits.