Estimation vs. Rounding

Date: 01/08/2002 at 11:21:31
From: Pam Langer
Subject: Estimation vs. rounding

On our testing we have questions about estimating answers and rounding 
answers. The two methods give different answers. 

How are the two methods different?

Date: 01/08/2002 at 13:06:43
From: Doctor Peterson
Subject: Re: Estimation vs. rounding

Hi, Pam.

Here's the simple answer: rounding means taking a known value and 
making it less accurate; estimation means coming up with an inaccurate 
number you didn't have in an exact form to start with.

So if I measure a table as 4 feet 1 inch wide, and call it 4 feet, I'm 
rounding. If I just look at it and say it's about 4 feet wide, I'm 
estimating.

You can use rounding as one step in estimation. To estimate the sum 
423 + 695, I might round both numbers to 400 + 700, and then add to 
get 1100. This result is an estimate of the sum of the original 
numbers. If I instead added directly to get the exact answer, 1118, 
and then rounded to get 1100, I would be rounding rather than 
estimating.

Often the two results will be different; rounding will be closer 
(given the same level of precision) because adding after rounding 
allows errors to accumulate. For example, I might estimate 444 + 649 
as 400 + 600 = 1000, when the exact answer is 1093, which rounds to 
1100. Knowing this, I would actually be careful not to round both 
numbers down, but would instead round 649 up (since it is so close to 
650), and get 400 + 700 = 1100 as a better estimate.

If what I've discussed is not quite the kind of problem you are 
dealing with, you might want to show me some specific examples so we 
can see where the difference arises.

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