Soldato
Because if you did this you would screw up all of the physics that I do, and probably a lot of other people's physics too
0.99r = 1
- Thread starter McDaniel
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Because if you did this you would screw up all of the physics that I do, and probably a lot of other people's physics too
Associate
It's the decimal equivalent of 1/2 = 2/4. It's something you don't generally get told but not all decimal numbers are actually different, it is a representation of a concept rather than the definition of the concept.
Because that's unnecessary and wrong.
Because most numbers would be thrown out. All numbers with terminating or repeating decimal expansions are rationals. Most Reals are not rational. Examples of non-rational (or rather irrational) numbers are pi, sqrt(2), exp(k) where k is any rational other than 0 etc.
In school students work predominantly with decimal expansions, rather than doing things algebraicly. When you study mathematics at university level you rarely actually work out what something looks like as a decimal. I didn't use a calculator at all at university. We were even banned from having them in exams, though they would have been of no use anyway. For example, if you have a square of side length 1 then the diagonal has length root(2). No mathematician would ever then reach for a calculator and then write down the decimal expansion as the answer (1.414...) because it's an imperfect representation of the perfect answer, root(2). But root(2) cannot be written as a terminating decimal in any base, it is irrational, a fact known to the Greeks 2000 years ago.
If you don't do any mathematics past age 16 then you could ask yourself "Why do I need to know about all of this?" because you don't need to know about concepts where a*b=b*a is false or where infinitely many objects is actually smaller than infinitely many other objects (Aleph Null < Aleph One) but mathematicians do and it feeds through into every area of physics and even many areas of computing and engineering.
New methods of encryption are built on the way in which there's infinitely many irrational points along elliptic curves. Computers are built using quantum mechanics, where a*b = b*a is false. New models of the universe are constructed which don't even have notions of space-time points, locations are meaningless on a fundamental level. These concepts might not be known to most people but they are everywhere, under the surface of all the technology around us.
Quite why some of the more ignorant people here believe that their C at GCSE maths a decade ago puts them in a position to make blanket assertions about concepts beyond their grasp I don't know. It always happens with 0.9r. You don't see the same people walking into a doctor's surgery and saying "You're prescribing the wrong drug!", they know they don't know enough biology, but given the years since their last maths lesson and poor test result suddenly they are experts! If they think this is 'advanced' mathematics or something which even troubles 1st year undergrads they have no idea what bleeding edge mathematics involves.
????
1/3 is represented as 0.3r in decimal notation - it is the same number, just represented differently 1/3 being a fraction 0.3r being the decimal representation
its got nothing to do with rounding, some numbers simply won't have a finite decimal representation - any rational number with a prime factor other than 2 or 5 will not be expressed as a finite decimal but will have a recurring decimal representation.
for example
1/9 = 0.1r
Associate
never seen this discussion on the forums on my travels but cool vid