Writing Decimals from Words

Date: 10/05/98 at 01:19:21
From: Lisa 
Subject: Writing decimals

Can you help me with my assignment? Here's a sample question:

Write the decimal for five hundred seventeen thousandths.                      

Please help,
Lisa

Date: 10/05/98 at 16:53:10
From: Doctor Rob
Subject: Re: Writing decimals

Lisa,

The first thing to do is to figure out where the fraction bar should 
go. The numerator will be a simple number, and the denominator will be 
a number with -ths on the end (like "three tenths": the numerator is
"three" and the denominator is 10 because of "tenths"). Since these are
specified to be decimals in the statement of the problem, the 
denominator will be a power of 10: tenths, hundredths, thousandths, 
ten thousandths, hundred thousandths, millionths, and so on. 

Figure out starting from the back where that part starts. Put the 
fraction bar just before that, and drop the "-ths" off the end. Then 
write the number before the fraction bar as the numerator, and the 
number after the fraction bar as the denominator. In your example:

   "five hundred seventeen thousandths"

since "seventeen thousandths" is not a power of 10, it cannot be the
denominator, so the fraction bar must go between these words. Then you
have:

   "five hundred seventeen / thousand"

or:

   517/1000

Now divide the denominator into the numerator by moving the decimal 
points of each to the left the same number of places as the number of 
zeroes in the denominator (in this case, three places left):

   .517/1.000 = .517

and that is your answer.

WARNING: Sometimes there are two answers, and you can't tell which is
correct. As an example, "One hundred ten thousandths" could mean
110/1000 = .110, or 100/10000 = .0100 (think about it). When the words 
are spoken, a slight hesitation indicates the position of the fraction 
bar, removing the ambiguity. The first would be pronounced as if it 
were written, "One hundred ten, thousandths," and the second as if it 
were written, "One hundred, ten thousandths."  Of course the comma is 
never written, just understood.

Good luck!

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