Using Hyphens to Indicate Place Value

Date: 08/30/2004 at 20:23:41
From: Joe
Subject: place value

What is the difference between the following two numbers:

five hundred thousandths
five hundred-thousandths

They seem the same to me, but my teacher says that they are different.
 The 1st one is written as 0.500, but I do not know how to write the
2nd one.

Date: 09/01/2004 at 09:59:50
From: Doctor Wilko
Subject: Re: place value

Hi Joe,

Thanks for writing to Dr. Math!  This is a great question and shows
why we should hyphenate the place value of decimal fractions.  You
might want to start by reviewing this from our archives: 

  Writing Numbers with Hyphens
    http://mathforum.org/library/drmath/view/63129.html 

If I ORALLY told you and a friend to write the number, "five hundred 
thousandths" you might write 0.500 and your friend might write 
0.00005.  Who would be correct?  Well, both of you could be--it's not 
clear which way I meant since they both SOUND the same. 

If I say (in writing) to write five hundred "thousandths", the place
value that I'm stressing is thousandths.  So, write the number 500 so
it ends in the thousandths place:  0.500

On the other hand, if I say to write five "hundred-thousandths", the
place value that I'm stressing here is the hundred-thousandths place.
So, write the number 5 so it is in the hundred-thousandths place: 
0.00005

Do you see the difference now?  The hyphen helps us decide if the
hundred is part of the thousandths, making it hundred-thousandths, or
part of the five, making it five hundred.  Since we don't speak the
hyphen, we often try to communicate it by using a slight pause as we
speak.  We might say:

  five....hundred-thousandths to mean 0.00005
  five hundred....thousandths to mean 0.500

Just to drive the point a little further, write these out as fractions 
and convert them to decimals.

  five hundred "thousandths" = 500/1000 = 0.500
  five "hundred-thousandths" = 5/100,000 = 0.00005

Does this help?  Please write back if you have further questions.

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