Choosing Appropriate Units

Date: 10/09/2003 at 22:29:58
From: Yana
Subject: How do you figure out things about measurement?

I don't get how to choose appropriate units for measurements.
For example, what units would you use to describe the size
of a garbage can?

Date: 10/10/2003 at 09:48:56
From: Doctor Ian
Subject: Re: How do you figure out things about measurement?

Hi Yana, 

Suppose someone asks you 

  1. The distance from Los Angeles to New York.

  2. The distance from your house to the one across the street.

  3. The distance from your elbow to your wrist. 

These are all examples of length, right?  And there are lots of
different units of length: millimeters, centimeters, meters, inches,
feet, yards, kilometers, miles, light years, city blocks, and so on. 

How do you know which units to choose?  Well, suppose you tried to
tell someone the distance from LA to NY in inches.  That would seem
silly, right?  Why?  Because the number would be enormous!  And people
have difficulty dealing with numbers that are really large. 

On the other hand, saying 'about 3000 miles' is something you can deal
with.  

What about the distance from your elbow to your wrist?  To express
that in miles would give you a really, really small number!  And
people have difficulty dealing with numbers that are really small.

But saying 'about 10 inches' is something you can deal with. 

What about the distance from your house to the one across the street?
Miles will give you too small a number; inches will give you too
large a number.  Feet might work, or yards.  

The point is, people strongly prefer numbers that aren't really big or
really small.  So this is why we _have_ so many different kinds of
units!  They let us keep the numbers manageable, regardless of whether
we're talking about the distance between two atoms (which might be a
dozen angstroms) or the distance between two stars (which might be a
dozen light years). 

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