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Question on Decimal points!


Rawhide Kids

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This may be elementary math, (But I did do well in math) so here it goes. I am wanting to go out and find a benchmark today. the coordinates are

N 41 37.58 W 91 11.405(NAD 83) My problem is on my Mag 330 to enter the .58 there is three decimal point instead of two i.e .058 I can not get rid of the third decimal point. Am I entering it right by putting the (0) in front of the 58 ( i.e. .058) is this the same coordinates as .58. if not how do I enter it or move my decimal point?

 

"I've heard there is no such thing as a ignorant question, only ignorant people who wont ask questions which in turn keep them ignorant."

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.580 is the same as .58. To enter 37.58, just enter 37.580. Each decimal place past the . represents so many tenths of the preceding place. 3.1 means 3 ones plus 1 tenth of a one. 3.3 means 3 ones and 3 tenths of a one. 3.58 means 3 ones plus 5 tenths of a one plus 8 tenths of a tenth (or 8 hundredths of a one.) 3.587 means 3 ones plus 5 tenths of a one plus 8 hundreths of a one plus 7 thousandths of a one. We could call that three and five-hundred eigthy seven thousandths (or just three point five eighty seven.) Good luck.

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Zero (0) is a legitimate number base. Maybe we could call it naughtical (though I like anal too.)I doubt that it is very useful, except perhaps in a geocaching puzzle.

 

Note that each number "position" to the left of the decimal has a "position value" of the base number raised to succesively higher powers starting with 1. Each number position to the right of the decimal has a position value equal to the base raised to succesively greater negative powers, starting with -1.

 

The value of a multi-decimal-position number is the sum of the products of each position value and the integer shown in that position that indicates how many of that position value there are to be added in.

 

The number 23.45 (base zero) would be 2 * 0^2 + 3 * 0^1 + 4 * 0^-1 + 5 * 0^-2, and this all equals 14 (base 10.)

 

The number 23.45 in base zero would be equal to 14 in base 10 because zero raised to any power, plus or minus, is 1. Therefore, this 23.45 (base zero) then equals 2 * 1 + 3 * 1 + 4 * 1 + 5 * 1 = 14 (base 10, decimal.)

 

Now just how useful do you find all that!

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Whoops, I goofed a little there. The powers of the number positions to the left of the decimal start with 0, not 1. In decimal they are 10^0, 10^1, 10^2 etc. Thus those decimal position values are 10^0 = 1, 10^1 = 10, 10^2 = 100 etc. To the right of the decimal they are 10^-1 = 1/10, 1o^-2 = 1/100 etc.

 

In the case of base zero, everything works as mentioned in my previous post above except for the first number position to the left of the decimal. That would be 0^0 (instead of 0^1) which I think is undefined! Maybe not. If 0^0 = 1 as does zero raised to anything else, then 23.45 naughtical would equal 14 decimal. If 0^0 is undefined, then 23.45 (or anything else) naughtical would be undefined as well.

 

Anybody out there have certain knowledge regarding whether 0^0 is defined or not?

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Regarding the naughtical numbver system, some might say you can't have a digit larger than one less than the base number, 1 for binary base 2, 7 for base octal 8, 9 for decimal base 10, E for hexidecimal base 12. If so, this would suggest you couln't have a naughtical number having digits larger than -1.

 

I don't see though why one couldn't conceive of a decimal number for instance, having digits greater than 9, such as (12)(9).(3)(16). This 4-position number would have a value of 12 * 10^1 + 9 * 10^0 + 3 * 10^-1 + 16 * 10^-2 = 120 + 9 + 0.3 + 0.016 = 129.316!

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quote:
Originally posted by Cachetrotters:

...and remember, it's only a decimal point because it's base ten. Base two would be a binary point, base eight would be an octal point, etc.... icon_biggrin.gif


 

But in any base it is still the radix point.

 

Dave_W6DPS

Nuclear Geo-Nerd

 

My two cents worth, refunds available on request. (US funds only)

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quote:
Originally posted by Don&Betty:

The number 23.45 (base zero) would be 2 * 0^2 + 3 * 0^1 + 4 * 0^-1 + 5 * 0^-2, and this all equals 14 (base 10.)

 

The number 23.45 in base zero would be equal to 14 in base 10 because zero raised to any power, plus or minus, is 1. Therefore, this 23.45 (base zero) then equals 2 * 1 + 3 * 1 + 4 * 1 + 5 * 1 = 14 (base 10, decimal.)


While interesting, it's incorrect. I won't try to argue against a base-zero number system, but the italicized phrase above is not true.

 

You have it backwards. Zero raised to any power is not 1. It is zero. Any number raised to the zero power is 1.

 

Jamie

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