h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Take an ordinary pocket calculator

key in 1 / 3

write down the answer

clear the memory

type in your answer the machine gave you and multiply by 3

any self respecting numerate person knows that if you divide anything by 3 and then muliply by 3 you get what you started with - not a pocket calculator;

according to this piece of bad technology

1 = 0.9999999

WHICH IS A LIE!!!!!!!!!!

Wait! I know the answer to this!

Take a look at a fraction like 1/9: in decimal form, it is .1111111 (repeating).

2/9: .2222222 (repeating)
3/9: .3333333 (repeating)
4/9: .4444444 (repeating)
5/9: .5555555 (repeating)
6/9: .6666666 (repeating)
7/9: .7777777 (repeating)
8/9: .8888888 (repeating)

The decimal form of a number divided by 9 then, is the number infinitely repeating behind a decimal point.

So, .9999999 (it only goes so far because the calculator only has so large a window) is the same thing as 9/9, which is the same thing as 1.


Shee

also, it's possible to prove that .2499999(repeating) = 1/4
.24999999*10 = 2.49999999
2.4999999999999 etc.
-.2499999999999 etc.
---------------
2.25 = (10 - 1) * 2.499999999
2.25 * 4 = 9
>8^B

Well, actually, it's just the calculator's inability to show more than eight characters, or as many characters you set it to show.

Remember, 1/3 is acually a very big number, with an endless display of .3333333

Your calculator doesn't really want to show you infinite threes, so it just displays the last eight digits.

What YOU did was take that ordinary pocket calculator and only worked with what it showed you. Any self-respecting numerate person knows that pocket calculators aren't very smart.

So, in any case, what you put in the calculator was not the answer to 1/3, but "0.3333333" or something to that affect. If you just left the answer alone, you would have gotten 1, because the calculator would remember that the answer to 1/3 was a repeting decimal.

So, in the end, it was the human that made the flaw, not the calculator. Which is always the case.

absolutely right
don't you feel sorry for ignoramouses-is that the right plural?- like that?
>8^B

Not always ... our numerical analysis lecturer told us about a calculator he once bought second hand that came with an 'errata'... there was one particular number (not especially large or anything) that the calculator couldn't display, it'd just show 'error' instead

yeah, the overflow?
it has only so many bits of memory and the largest number is 2^n - 1 where n is the bit depth
you probably got something like 1.8446744e+21
>8^B

Nope -- not the overflow... that's the point

It just happened to be a quirk of the particular floating-point representation the calculator used...

(hmm, and that would work for integers -- but calculators don't use integers... the real max is 0.11...111*2^(max exponent) -- the max exponent is probably close to a power of two, but they're not a straight integer representation either... check this out if you're interested: http://www.psc.edu/general/software/packages/ieee/ieee.html)

oh, yeah
ur right
swy
>8^B

Also try 1.111111111/9 on your calculator, giving 0.1234567901...
(usually).

Work it out by hand.

Now its 0.123456789..., which is what its supposed to be.

A microchip older than Pentium 4 usually gets it right.

A problem of a bad algorithm predisposing to cumulative errors originating with Pentium 4.