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Writing Numbers with Hyphens

Date: 06/04/2003 at 16:25:36
From: Brian
Subject: Writing numbers with hyphens

Why do we hyphenate one hundred-millionth, but we don't hyphenate one 
hundred million?

Date: 06/04/2003 at 19:33:13
From: Doctor Greenie
Subject: Re: Writing numbers with hyphens

Hi, Brian -

I'm not an expert on this, but I know why I think this is the case.

When we say "one hundred million," the 'unit' of measure is millions, 
and we are counting one hundred of them.

When we say one hundred-millionth, the 'unit' of measure is neither 
hundreds nor millionths; it is hundred-millionths, and we are counting 
one of them.

- Doctor Greenie, The Math Forum 

Date: 06/05/2003 at 11:07:52
From: Doctor Peterson
Subject: Re: Writing numbers with hyphens

Hi, Brian.

Here is another perspective on the same basic idea Dr. Greenie 
expressed. To make it a little clearer at some points, I will use 
"two hundred-millionths" as my example.

We COULD hyphenate two hundred million as two-hundred million, or as 
two hundred-million, or even as two-hundred-million, if we wanted to, 
and it wouldn't change the meaning, which is two times a hundred 
times a million. We don't do so because it isn't necessary; 
multiplication is associative.

  200,000,000 = 2 * 100 * 1,000,000        two hundred million

But the fraction is different: it means not two times a hundred times 
a millionth, but two times a (hundred millionth); or alternatively, 
two divided by a (hundred million). Just as in algebra we use 
parentheses to group the parts that must be kept together, in English 
we hyphenate them, turning "hundred millionth" into a single word.

  2/100,000,000 = 2 / (100 * 1,000,000)    two hundred-millionths

  200/1,000,000 = (2 * 100) / 1,000,000    two-hundred millionths

In the latter case we probably would not hyphenate as I showed, for 
the same reason we don't have to parenthesize the expression; we 
assume that numbers are grouped from left to right if not otherwise 

So we hyphenate the fraction because division is not associative! 
English is not quite as irrational as it often seems.

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

- Doctor Peterson, The Math Forum 
Associated Topics:
Elementary Definitions
Elementary Fractions
Elementary Large Numbers

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