Place Value and Similar Numbers

Date: 08/15/2003 at 15:40:33
From: Mrs. Fansler's 6B Math Class
Subject: Place value

How do you read this number: 10.00001?

We were confused because when you read 10.100 you would say "Ten and 
one hundred thousandths."  We believe that when you read 10.00001 it 
would sound the same.

We are guessing that the number would sound the same but you would 
write each one differently. For example:

10.100 would be written: Ten and one hundred thousandths
10.00001 would be written: Ten and one hundred-thousandth.

We would like to know if this is correct.

Date: 08/15/2003 at 16:03:20
From: Doctor Peterson
Subject: Re: Place value

Hi, Class! Thanks for a good question.

I would like to change your question a little to make it harder. The 
trouble with what you asked is that 10.100 is read as "Ten and one 
hundred thousandths" with an "s" on the end, so the two DO sound 
different. Instead, let's use

  10.200 = Ten and two hundred thousandths
  10.00002 = Ten and two hundred-thousandths

Here both are plural, but as you noted, the only difference is the 
presence of a hyphen, which in reading might mean only that you leave 
a slightly smaller gap between the words. To make the difference 
stronger, I might tend to say (or even write)

  10.200 = Ten and two-hundred thousandths

and exaggerate the difference as much as I could.

You're right; there is very little difference. Two details rescue us 
from having an unusable number system:

1. We rarely say 10.200; usually it would be called 10.2 (though 
there are reasons for including the extra zeroes, when you get to 
studying significant digits).

2. In reality (as opposed to elementary school) we would read the 
numbers as

  10.200 = Ten point two-zero-zero
  10.00002 = Ten point zero-zero-zero-zero-two

This is much easier to say as you read it, easier to figure out when 
you hear it, and easier to copy down. Who cares if a lot of teachers 
would say it's illegal!

If you have any further questions, feel free to write back.

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