place values once more
- From: mayhousered@xxxxxxxxx
- Date: 12 Mar 2007 20:38:51 -0700
http://groups.google.com/group/sci.math/browse_thread/thread/57168087b028599f/6a65dbfa2655222d?hl=en#6a65dbfa2655222d
An earlier post sought an explanation of why the first place to the
right of the decimal is tenths and not "oneths" or something of that
sort.
Putting aside proofs, intuitive-type explanations were given that the
reason (roughly rephrasing) is that 1 is a foundational unit, and thus
the unit that gets built up or cut up into tenths, hundredths, and so
on.
That is, we start with 1, and then times it by tens moving leftward,
and divide it by tens moving rightward... so there is no "oneth", or
opposite operation of what produced 1.
The explanatory posts were good and helpful. But now a different issue
arises. It is inconsistent to write the 1 in the same "field" (to the
left of the decimal) as the products (10,100,...) are written in. If 1
is foundational, and not the result of some operation as the others
(10,100, .1,.100) are, then it shouldn't be either to the right OR
left of the decimal. It should, maybe, sit squarely on top of it
(picture a '1' written over a period) or there should be a decimal
point both before and after the 1 (picture dot-1-dot).
Of course this issue of syntax is much ado about something purely
conventional and arbitrary (the way we right 1 and then a decimal
point)... but I think it should be added to the earlier explanations
since the original question (not a rare one for early-level ponderers
of math I think) arises not out of any confusion over the results of
multiplying or dividing by tens, but specifically out of the way we
have chosen to write such numbers.
..
.
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