The Importance of Units in Math Calculations and Answers

Date: 10/13/2005 at 12:13:05
From: Samier
Subject: Units

I do not understand why we would even use units.  What is the point?
I find everything confusing.  I don't know what units are.  I think
they are used to label answers.  Please help me.

Date: 10/13/2005 at 12:21:28
From: Doctor Ian
Subject: Re: Units

Hi Samier,

Suppose you want to know how long it will take you to get from your
house to some other place.  You ask me, and I say, "It will take 5."

  5 what?  5 minutes?  5 hours?  5 days?

We use numbers to represent stuff in the world.  Sometimes it's just
counting, e.g., 

  I found 9 mushrooms today.
  I found 18 yesterday.
  So now I have 9 + 18 = 27 mushrooms.

But sometimes we're using numbers to represent things that we measure,
like distances or weights or areas:

  I have a board 12 feet long.  
  I want to cut it into pieces 3 feet long. 
  I can cut it into (12 feet) / (3 feet per piece) = 4 pieces.

We can use different ways of measuring something, e.g., 

  I have a board 144 inches long. 
  I want to cut it into pieces 3 feet long.

If I just divide 144 by 3, without paying attention to units, I get an
answer of 48.  But what does it mean?  It's the same problem as
before, since 144 inches is the same thing as 12 feet!  So I'd better
get the same answer--4 pieces, not 48.  To get the same answer, I have 
to change my units:

  I have a board 144 inches long.
  I want to cut it into pieces 36 inches long.
  I can cut it into (144 inches) / (36 inches per piece) = 4 pieces.

So units are how we make sure that our calculations about the world
make sense. 

Does this help? 

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

Date: 10/13/2005 at 13:13:47
From: Samier
Subject: Thank you (Units)

Thanks a lot, Doctor Ian.  Now I understand why we use units.

Samier