Percentages
-----------

The `M-%' (`calc-percent') command takes a percentage value, say 5.4,
and converts it to an equivalent actual number.  For example, `5.4
M-%' enters 0.054 on the stack.  (That's the META or ESC key combined
with `%'.)

Actually, `M-%' creates a formula of the form `5.4%'.  You can enter
`5.4%' yourself during algebraic entry.  The `%' operator simply
means, "the preceding value divided by 100."  The `%' operator has
very high precedence, so that `1+8%' is interpreted as `1+(8%)', not
as `(1+8)%'.  (The `%' operator is just a postfix notation for the
`percent' function, just like `20!' is the notation for `fact(20)', or
twenty-factorial.)

The formula `5.4%' would normally evaluate immediately to 0.054, but
the `M-%' command suppresses evaluation as it puts the formula onto
the stack.  However, the next Calc command that uses the formula
`5.4%' will evaluate it as its first step.  The net effect is that you
get to look at `5.4%' on the stack, but Calc commands see it as
`0.054', which is what they expect.

In particular, `5.4%' and `0.054' are suitable values for the RATE
arguments of the various financial functions, but the number `5.4' is
probably *not* suitable--it represents a rate of 540 percent!

The key sequence `M-% *' effectively means "percent-of."  For example,
`68 RET 25 M-% *' computes 17, which is 25% of 68 (and also 68% of 25,
which comes out to the same thing).

The `c %' (`calc-convert-percent') command converts the value on the
top of the stack from numeric to percentage form.  For example, if
0.08 is on the stack, `c %' converts it to `8%'.  The quantity is the
same, it's just represented differently.  (Contrast this with `M-%',
which would convert this number to `0.08%'.)  The `=' key is a
convenient way to convert a formula like `8%' back to numeric form,
0.08.

To compute what percentage one quantity is of another quantity,
use `/ c %'.  For example, `17 RET 68 / c %' displays
`25%'.

The `b %' (`calc-percent-change') [`relch'] command calculates the
percentage change from one number to another.  For example, `40 RET 50
b %' produces the answer `25%', since 50 is 25% larger than 40.  A
negative result represents a decrease: `50 RET 40 b %' produces
`-20%', since 40 is 20% smaller than 50.  (The answers are different
in magnitude because, in the first case, we're increasing by 25% of
40, but in the second case, we're decreasing by 20% of 50.)  The
effect of `40 RET 50 b %' is to compute `(50-40)/40', converting the
answer to percentage form as if by `c %'.