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#1 2021-12-12 14:52:12

Hannibal lecter
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Registered: 2016-02-11
Posts: 330

why subtract this kinky number is equal 1

hi, why 1 - 1.928749848×10^(-22) equal = 1 in online calculators?
I used also google calculator :-
I tried to remove the 1 integer to become 0.928749848×10^(-22)
but still the same the sum equal 1! is there something wrong?

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#2 2021-12-12 15:27:04

Mathegocart
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Registered: 2012-04-29
Posts: 2,199

Re: why subtract this kinky number is equal 1

This inaccuracy derives from how computers represent real numbers, after all, computers handle and tinker around with binary numbers and mathematics, and it is impossible to represent all real numbers in binary, and this leads to a plethora of idiosyncracies; another one is that tan(pi/2) will not yield infinity not result in an overflow in the typical floating-point representations; if you type tan(pi/2) into a humble calculator that is not programmed with these cases in mind, the result will be

. In particular, there does not seem to be a high level of precision in these calculators that are specifically designed with general-purpose calculations.

Last edited by Mathegocart (2021-12-12 15:27:15)


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#3 2021-12-12 15:29:49

ganesh
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Registered: 2005-06-28
Posts: 35,588

Re: why subtract this kinky number is equal 1

Hi,

The number gives the solution 1 in a scientific calculator too.

1 - 1.928749848×10^(-22) = 1.

This is because the resultant produces rounding off; for all practical purposes, this would apply.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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#4 2021-12-13 00:01:58

phrontister
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From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,700

Re: why subtract this kinky number is equal 1

MIF has a 'full precision' calculator here, that gives the 'full precision' answer 0.9999999999999071250152, which is accurate to the 22 decimal places present in the sum.


"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#5 2021-12-13 00:47:18

ganesh
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Registered: 2005-06-28
Posts: 35,588

Re: why subtract this kinky number is equal 1

Hi,

That's right!

The MathIsFun website has elucidated in these cases.

Full Precision Calculator does the work.

1 - 1.928749848×10^(-22) produces 0.9999999999999999999998071250152.

It again shows the brilliance of the website, and the creator.

Thanks, phrontister!


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#6 2021-12-13 00:53:59

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,700

Re: why subtract this kinky number is equal 1

I've learnt from you, ganesh! You often give links to MIF's tools! up


"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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