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### Why Estimate?

```Date: 08/16/2002 at 11:14:49
From: Stephanie
Subject: Estimation

Estimate to the nearest thousand a solution to Dave's subtraction
problem. The numbers are:

6,107
-2,980
-----
4,127

I just don't know how to estimate.
```

```
Date: 08/16/2002 at 12:10:25
From: Doctor Peterson
Subject: Re: Estimation

Hi, Stephanie.

Assuming that 4,127 is "Dave's" answer to the problem, it illustrates
why it can be very important to estimate - it's wrong, it's an easy
mistake to make, and it would have a huge effect on whatever he uses
the number for, from spending money to building a house. And
estimating makes it easy to see the error!

To estimate to the nearest thousand, the natural thing to do is to
round the numbers you are adding to the nearest thousand. Which of
these numbers is closest to 6,107?

0   1000 2000 3000 4000 5000 6000 7000 8000 9000

Which of those numbers is closest to 2,980?

Now subtract those much simpler numbers, and the result is your
answer. Sometimes you can get a better estimate by thinking about how
much you increased or decreased each number when you rounded them, and
how that will affect the result; but in this case the difference of
the rounded numbers is good enough.

Rounding Numbers
http://mathforum.org/dr.math/faq/faq.rounding.html

For more on estimation, see

Estimating Sums By Rounding
http://mathforum.org/library/drmath/view/59021.html

If you need more help, please write back and show me how far you got.

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