How this calculator works
Scientific notation separates a signed coefficient with magnitude between 1 and 10 from an integer exponent. The containing-decade convention uses that exponent. A nearest-power convention switches to the next exponent at a coefficient of sqrt(10), the midpoint on a logarithmic scale. Zero has no finite logarithmic scale.
Formula
x = a × 10^e, with 1 <= |a| < 10. Decade order = e. Nearest logarithmic order = e + 1 if |a| >= sqrt(10), otherwise e.
Worked example
4500 = 4.5 × 10^3: its containing decade is 10^3 and its nearest logarithmic power is 10^4. For 0.002, scientific notation is 2 × 10^-3 and both orders are -3.
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Frequently asked questions
Why do sources give different orders?
Some use the scientific-notation exponent, while others choose a nearby power of ten. Select and state your convention when comparing results.
Do negative inputs have an order?
Their absolute magnitudes do. The sign remains in the scientific coefficient.
Why show 10 raised to an exponent as text?
Text can represent extreme scales, including 10^-324, that would underflow an ordinary numeric output.