terminology of differences

Question

When quantity a changes to b, it can be said that the difference is d = b - a. I might call this the subtractive difference. Example: Let a be 0.02 and b be 0.03. Then d = 0.03 - 0.02 = 0.01. Applying the difference is a matter of adding to the base value. a + d = 0.03.

Also, it can be said that there is a difference d = (b/a) - 1. So for example the difference when quantity a = 0.02 changes to b = 0.03, is 0.5, or half of the base value. The difference is applied to the base value. Example: a (1+d) = 0.03. What is the name for this kind of difference?

When the quantities are measures of change, sometimes people calculate the difference between 0.02 and 0.03 as d = ((1+b)/(1+a)) - 1. The difference is 0.009804 and to apply it, the measure of change 0.02 and the measure of change 0.009804 are both applied to some (unspecified) base, resulting in a measure of change of 0.03. Example: (1+a)(1+d) - 1 = 0.03. What is the name for this kind of difference?

Note that the difference between 0.02 and 0.03 has been variously described as being +0.01, +0.5, and +0.009804.

Unambiguous terse software generated prompts for perpetually puzzled people is the practical application for the names that would be given to these differences.

Answer 1

Too long for a comment:

The point is the context, and it is more important to be clear about what the change is than to find names for the particular measure of change. For example if these are interest rates or something similar:

1. Let us suppose this is an interest rate of $2\%$ changing to $3\%$. Calling this a $1\%$ increase is ambiguous as you have identified, but most people would accept that it is "an increase of $1$ percentage point".

2. Again let us suppose this is an interest rate of $2\%$ changing to $3\%$. Calling this a $50\%$ increase is ambiguous as you have identified, but most people would accept that the new interest rate is "$1.5$ times" the previous interest rate or perhaps "half as much again".

3. The last example is related to compounding: if the interest rate is $2\%$ for the first part of the period and $3\%$ in total over the period then (using compounding), the interest rate for the second part of the period is about $0.98\%$ since $1.02 \times 1.0098 \approx 1.03$, and $0.98\%$ might be understood if called something like the "further compounded increase", though possibility of this causing total blankness is high as most people do not naturally understand compounding.