diff --git a/core/numeric/convert.xml b/core/numeric/convert.xml index 27174fa0..c5a056a2 100644 --- a/core/numeric/convert.xml +++ b/core/numeric/convert.xml @@ -413,4 +413,3 @@ - diff --git a/core/numeric/percent.xml b/core/numeric/percent.xml new file mode 100644 index 00000000..499c747c --- /dev/null +++ b/core/numeric/percent.xml @@ -0,0 +1,94 @@ + + + + + + + + Converting between real and~percent is trivial: + + $$ + \begin{align} + r &= p\over100; + p &= 100r. + \end{align} + $$ + + ^[Percent difference] (also called ^[relative change]) describes + the~change in value as a~percentage (for example: $10$~is $50%$ + of~$20$, and is~$100%$ of~$5$). ^[Percent change] recognizes the + direction of the change (that is---$10$ is~$20$ reduced by~$50%$, so + $p=-50$). + + Since ``change'' sounds like a~verb eclarative contexts, we use + the~term ^[percent difference] to mean ^[relative change]; it is + defined as: + + $$\delta \over x = {{x_\beta - x_\alpha}\over{x_\alpha}} \times 100 = p.$$ + + Notice that this preserves the direction of the change. So, in the + context of the previous example, we can say that $10$ + \emph{reduces}~$20$ by~$50%$, giving~$p=-50%$. + + + + diff --git a/core/test/core/numeric/percent.xml b/core/test/core/numeric/percent.xml new file mode 100644 index 00000000..36169fc1 --- /dev/null +++ b/core/test/core/numeric/percent.xml @@ -0,0 +1,142 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + These tests are similar to the above, except that they represent + the~percent difference between two values. That is, given the + values $5$~and $15$, we arrive at a~$200%$ increase. So + if~$p=200$, then we want $5r=15, r=3=\((15-5)/5\)+1$. + + + + + + + + + + + + + + + + + Similarly, if we go from~$10$ to~$5$, we have~$p=-100$ + and~$10r=5$; then~$r=1/2=0.5$. + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/core/test/core/suite.xml b/core/test/core/suite.xml index cab01254..64e14f76 100644 --- a/core/test/core/suite.xml +++ b/core/test/core/suite.xml @@ -28,6 +28,7 @@ +