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Decimal points


Notexceling
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Mind my stupidity 

 

If the number "1" explains itself and every other number,

 

 but, it's restricted to 100%, 

 

( 1 = 100%)

 

then

 

Wouldn't that mean that the decimal value greater than 1 is part of another "(1)"?

e.g

 

1.1

 "(1)+(.1)"

 

Even though it is developed with the original number, it has exceeded the boudaries of 100%

I thought that " .1" must be part of another one that only has "(0.9)" remaining, only because of "(1)" being restricted to (100%).

 

Another example

 

3.1415926535...

(1)+(1)+(1)

We have "3"  individual 100% complete numbers, but I always thought that the next "1", or the 4th "1" is now only 0.9695184575...

 

Am I wrong?

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  • 3 weeks later...

Mind my stupidity

 

If the number "1" explains itself and every other number,

 

but, it's restricted to 100%,

 

( 1 = 100%)

 

then

 

Wouldn't that mean that the decimal value greater than 1 is part of another "(1)"?

e.g

 

1.1

"(1)+(.1)"

 

Even though it is developed with the original number, it has exceeded the boudaries of 100%

I thought that " .1" must be part of another one that only has "(0.9)" remaining, only because of "(1)" being restricted to (100%).

 

Another example

 

3.1415926535...

(1)+(1)+(1)

We have "3" individual 100% complete numbers, but I always thought that the next "1", or the 4th "1" is now only 0.9695184575...

 

Am I wrong?

 

I think I see what you're getting at.

 

In your example "3.14159.....", each numeral represents either a "1", or a multiple of "1" - as "3" represents "1"+"1"+"1". All units.

 

No numeral represents a subdivision, of the unit "1". The decimal point may give an impression of such subdivision. But in reality, there are only whole units in any number. For example, the number "0.14" means 14 units out of 100 units. Always the basic units are "1"s, and quite indivisible.

 

This would be clearer, if we used fractional notation and wrote "14/100"

 

The "damn dot" confuses our thoughts! (Convenient though it may be for succinct arithmetic)

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Just to pursue this a little further:

 

In base-10 decimal maths, we find that the "decimal point" helps - for example, it distinguishes 3.14 from 31.4

 

But suppose instead we used base-2 maths. So all our numbers were strings of 0's and 1's. Like 100111010.

 

In a base-2, binary system - would a "binary point" be of any help - or even of any meaning?

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Just to pursue this a little further:

 

In base-10 decimal maths, we find that the "decimal point" helps - for example, it distinguishes 3.14 from 31.4

 

But suppose instead we used base-2 maths. So all our numbers were strings of 0's and 1's. Like 100111010.

 

In a base-2, binary system - would a "binary point" be of any help - or even of any meaning?

 

the first unit after the "binary point" could be halves, the next quarters, the next eights etc.

 

3.14 would be approximated by 11.001001

ie 2+1+1/8+1/64

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Just to pursue this a little further:

 

In base-10 decimal maths, we find that the "decimal point" helps - for example, it distinguishes 3.14 from 31.4

 

But suppose instead we used base-2 maths. So all our numbers were strings of 0's and 1's. Like 100111010.

 

In a base-2, binary system - would a "binary point" be of any help - or even of any meaning?

You can't pursue it further because you have not made a start.

The first thing you said

"If the number "1" explains itself and every other number,"

does not make sense.

 

In what way does 1 explain itself?

How can you say that 1 explains 42?

You are just making word salad.

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the first unit after the "binary point" could be halves, the next quarters, the next eights etc.

 

3.14 would be approximated by 11.001001

ie 2+1+1/8+1/64

 

Thanks imatfaal. I notice that you say the binary point "could" serve to distinguish halves, quarters, eighths etc. I understand that. It would certainly be useful to humans.

 

But what about computers, which operate on binary numbers. Doesn't this binary system mean that computers, at their deepest working level, can only recognise two entities - either "0" or "1". Is that true?

 

If it is, how can they be made to recognise a third entity - the Point , or "."? Or don't they need it?

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Computers don't recognize they process. A computer does not take a square root - it follows a procedure dictated by its programming. I have no idea how computers know where the instruction ends and the operand begins - but I would guess that every instruction contains a section which indicates that the next x binary digits are the first operand and the following y are second operand; it would be simple to instruct the computer to treat the first 16 digits as the number and the next 16 as the binary fraction

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Ah so the number provided to the computer has a section which specifies where the "binary point" would lie - that seems to be sensible and more efficient

 

So with a binary number, it's possible to specify the location of the "binary point", using just the binary numerals - 0 and 1

 

Could the same be done with a decimal number - ie, specify the location of the "decimal point", using just the decimal numerals 0 to 9.

 

If so, do we really need the non-numeral symbol - the "."?

Edited by Dekan
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If you convert numbers to standard index form

http://www.bbc.co.uk...otshirev1.shtml

the decimal point is redundant.

 

I've studied the link you kindly provided - thanks!

 

But the link does show, that Standard Index has decimal points in it. Plus signs like "x" - and small superscript numbers like "6".

Can these "x"'s and superscripts be written in binary computer code - bearing in mind that computers can only recognise (or as Imatfaal previously clarified, "process") - 0's and 1's - nothing more! What would a Standard Index look like in Binary?

 

This is what I find hard to understand. If computers can do every mathematical calculation using just "0" and "1", why aren't we doing it too?

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The decimal point is redundant because it's always the second character. The same sort of thing is true of the X10^

However you still need some character to distinguish the mantissa from the exponent unless you decide (in advance) how many digits the mantissa will be.

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If computers can do every mathematical calculation using just "0" and "1", why aren't we doing it too?

 

Decimal is just a convention. There have been societies that developed mathematics using base 20 (Mayans), base 60 (Babylonians), or base 6 (Ndom language in Papua New Guinea). I am sure there are others. And there is no reason you can't do all your math in base 2. Just know that most of the rest of the world is going to expect base 10 answers.

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Old joke alert!

There are 10 sorts of people in the world; those who understand binary; those who understand ternary,and those who don't.

 

My 'phone number (just the local bit of it) is 7 digits long. In binary it would be 22 digits, and I'd never remember it.

On the other hand, in base 9999999 it would only be 1 digit, but I'd need to remember the values and order of 9999999 digits.

Base 10 is a compromise and relates to nothing more significant than our having 10 fingers.

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