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### 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.

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

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/
```
Associated Topics:
Elementary Fractions
Elementary Place Value

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