Relative Change and Difference - Other Change Units

Other Change Units

Change in a quantity can also be expressed logarithmically using the unit of logarithmic change: the neper (Np). Normalization with a factor of 100, as done for percent, yields the derived unit centineper (cNp) which aligns with the definition for percentage change for very small changes:


D_{cNp} = 100 \cdot \ln\frac{V_2}{V_1} \approx 100 \cdot \frac{V_2 - V_1}{V_1} = \text{Percentage change} \text{ when }\left | \frac{V_2 - V_1}{V_1} \right | << 1 \,

But using cNp has two additional advantages. First, there is no need to keep track of which of the two quantities, V1 or V2, the change is expressed relative to, since, under the conditions of the approximation, the two quantities are nearly the same. Second, an X cNp change in a quantity following a -X cNp change returns that quantity to its original value. For example, if a quantity doubles, this corresponds to a 69cNp change (an increase). When it halves again, it is a -69cNp change (a decrease.)

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