place values

[mayho...@yahoo.com]

We of course are all very comfortable and familiar with the
following...

that the first "slot" or place left of the decimal point is for the
ones, and that the second place is for the tens, and the third place
for the hundreds, and so on.
But why is the first place to the right of the decimal for the tenths
and not the oneths?

[karl]

You have for a number x the decimal expansion:

x = a_n * *10^n +...+ a_3 * 10^2 + a_2 * 10^1 + a_1 * 10^0 + a_{-1} * 10^{-1} + a_{-2} * 10^{-2}...

written as

x = a_n...a_2 a_1 a_0 , a_{-1} a_{-2} ..

There are no oneths as you call them.

Ciao

Karl

[Rainer Rosenthal]

Because a oneth is a one. See: 1/1 = 1.
And as the ones already have their place, it would be unfair to
offer them a second place, wouldn't it?

And then there are historical reasons:
We all learned that Pi = 3.1415926. Think of all the money and confusion
spent on rewriting this as Pi = 3.31415926.

And there would be other threads like "Is 0.9999... really 1?", asking
"Is 0.09999... really 1?" or even worse: "Is 0.09999... really 1.1?".

And after the revolution someone might stand up and ask: "Why the hell
do I have to believe that 1 = 1.1?".

Best regards,
Rainer .
. .
_________________________.___.___._______________________
Rainer Rosenthal . . r.ros...@web.de
.

[Nick]

<mayho...@yahoo.com> wrote in message
news:1173422878....@j27g2000cwj.googlegroups.com...

I agree with Rainer.

It goes hundreds, tens and units, tenths, hundredths etc

Oneths equivalent to units.

Power of 10

3 2 1 0 | -1 -2 -3

Hund Tens Units Tenths Hund
reths

In a sense the units are the centre of things.

.1 is 1/10 and as I have indicated the reciprocal of 10.

1 is its own reciprocal.

Nick