Free · Scientific notation
Decimal Order and Scientific Coefficient
Express a signed nonzero decimal as a normalized scientific coefficient and a power of ten.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
34000 = 3.4 × 10^4, with decimal order 4.
number = coefficient × 10^exponent; exponent = floor(log10(abs(number)))
Worked example
Enter these known values and leave the other values blank.
- Number
- 34000
- Result
- Scientific form: 3.4 × 10 to the exponent 4. Decimal order: 4.
Assumptions and limitations
- The order is the exponent in normalized base-ten scientific notation, not a nearest-power convention. The magnitude of the coefficient is at least one and less than ten.
- Zero is excluded by the captured input domain. Inputs retain the source nonzero magnitude bounds. Negative values use a negative coefficient with the magnitude exponent.
Common questions
What is the order of a small decimal?
It is the normalized base-ten exponent. For example, 0.004 = 4 × 10^-3, so the order is -3.
Does a negative sign change the order?
The sign stays in the coefficient. The order uses the absolute magnitude.
References
- Scientific notation definition
- Scientific notation definition
- Calculation definition and unit reference
Translate scientific exponent and mantissa from the captured Number/string helper into local decimal logarithm, exact floor and power-of-ten arithmetic. Retain the nonzero captured magnitude domain, signed coefficient, forward-only outputs and full-precision scientific result note. Evaluate the same original strict magnitude bounds through exact differences and sign, so tiny valid inputs are not falsely rejected by floating comparison tolerance.