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Why Estimate?

Date: 09/16/2002 at 17:10:15
From: Tyler Smith
Subject: Estimation

Why do we use estimation?


Date: 09/16/2002 at 18:34:32
From: Doctor Ian
Subject: Re: Estimation

Hi Tyler,

The _point_ of estimating things is that estimating will save you 
space, time, or effort, and in return for those savings, you agree to 
pay a price in accuracy. 

There are lots of different ways to estimate things: you can eliminate 
digits from a number (truncation or rounding), you can replace a 
decimal number with a fraction (which, technically, is the same 
thing), you can replace any number with a 'nearby' number that's 
easier to work with, you can use a graph to replace a list of 
individual values, you can use a simple function in place of a more 
complicated function, and so on.

In each case, you're making a trade-off: "It's not going to hurt much 
if my answer is off by a little bit, especially if I can get that 
answer ten times more quickly, or by storing a thousand times less 
information."

The _art_ of estimating things properly requires two different sets of 
skills.  The easier one is learning the various techniques of 
estimation: rounding, graphing, and so on.  The harder one is learning 
to recognize how much accuracy you can afford to throw away in a given 
situation, and how much benefit you'll get from doing it.

Does this help? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/ 
Associated Topics:
Middle School About Math
Middle School Number Sense/About Numbers

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