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### Opposite of Percentage

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Date: 07/31/2001 at 20:45:01
From: Marty Ryerson
Subject: Term for the "opposite" of percentage

Hi,

I am beginning to wonder if there *is* an answer to this.

I am trying to write a document explaining a common procedure, namely,
calculating a discounted price. To calculate the discount, you
multiply the "base" by the "percent discount" to yield "percentage."
At least, these were the terms I was taught.

So, if the price is \$32 and the discount is 15%, then you multiply 32
times .15 to get the amount that is to be subtracted from the initial
price (\$4.80) to yield the discounted price (\$27.20). I have been
taught that the "initial price" (\$32) is the "base," the .15 is the
"percent" or "discount rate," and the resulting discount amount
(\$4.80), is the "percentage."

Another way to calculate the final price would be to subtract the
percentage from 100 (100% - 15% = 85%) and then multiply that result
by the original price (.85 times \$32 = 27.20).  Or, as it appears in
many computer programs, net = price * (1-discount_rate), where it is
understood that discount_rate is a decimal fraction.

My question is one of terminology. What is the name given to the term
"(1-discount_rate)" in this example? I have looked up reciprocal,
complement, inverse, etc., but none of those fits. I need to be able
to define this word once and then use it repeatedly in my document,
rather that explaining it every time I use it, which will be many
times.

Thanks for any help.

Marty
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Date: 07/31/2001 at 22:39:23
From: Doctor Peterson
Subject: Re: Term for the "opposite" of percentage

Hi, Marty.

What you want is "the complement of the discount rate." Here is one
site I've found that defines it:

http://courses.confederationc.on.ca/bm105/part2/unit7/bm7s1.htm

Trade discounts are used in the retail sector. They are used to
calculate how much a retailer will pay a manufacturer for a given
product...

Complement of a Trade Discount: This is the difference between the
discount rate and 100%. The complement can be any percent that
results when you subtract the trade discount rate from 100%.

In general mathematicians use the word "complement" to mean "all
except ..." or "the whole minus a given part"; here it means 1 minus a
fraction - though I haven't found any dictionary that gives this
definition.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
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