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### Percentage Target (Projection)

```Date: 07/24/2003 at 05:34:41
From: Sol
Subject: Percentage target (projection)

Hi there,

I am trying to work out percentage difference between a given figure
and a projected figure in the future.

For example, say in 2000 I have a percentage of 90.4%, and by 2003 I
need to work out a 10% decrease in my original figure.

I work out a 10% decrease of 90.4% to be 80.4%, but I know this is not
correct.

Thank you.
```

```
Date: 07/25/2003 at 11:26:51
From: Doctor Greenie
Subject: Re: Percentage target (projection)

Hi, Sol -

There are two distinct ways of thinking of a 10% decrease.  Because
of the word "decrease" (I suppose), most people think of a 10%
decrease as the original amount minus 10% of the original amount.
However, in most cases, the arithmetic required to work with
percentages is easier if, instead, you think of a 10% decrease as
meaning that 90% is left.

So if you are starting with a figure of 90.4%, then a 10% decrease
from that means you have 90% of the 90.4% left:

(.90)*(.904) = (.8136) = 81.36%

You noted that you didn't think 80.4% was the correct figure; you are
right. It is not the right figure because you subtracted 10% of
the "original total" instead of 10% of the 90.4% you started with.
The alternative to the above calculation is to subtract 10% of the
90.4% from the 90.4% you started with:

.904 - (.10)*(.904) = .904 - .0904 = .8136 = 81.36%

I hope this helps. Please write back if you have any more questions

- Doctor Greenie, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Fractions

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