## A Conversation for Mathematics

### The calculator's inherent inability to count

Sean Started conversation Feb 12, 2002

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!!!!!!!!!!

### The calculator's inherent inability to count

the Shee Posted Mar 28, 2002

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

### The calculator's inherent inability to count

Calculator Nerd 256 Posted Jul 26, 2002

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

### The calculator's inherent inability to count

U198950 Posted Aug 6, 2002

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.

### The calculator's inherent inability to count

26199 Posted Jan 10, 2003

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

### The calculator's inherent inability to count

Calculator Nerd 256 Posted Jan 21, 2003

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

### The calculator's inherent inability to count

26199 Posted Jan 21, 2003

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

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

### The calculator's inherent inability to count

26199 Posted Jan 21, 2003

(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)

### The calculator's inherent inability to count

ITIWBS Posted Apr 15, 2015

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.

Key: Complain about this post

### The calculator's inherent inability to count

- 1: Sean (Feb 12, 2002)
- 2: the Shee (Mar 28, 2002)
- 3: Calculator Nerd 256 (Jul 26, 2002)
- 4: U198950 (Aug 6, 2002)
- 5: Calculator Nerd 256 (Aug 7, 2002)
- 6: 26199 (Jan 10, 2003)
- 7: Calculator Nerd 256 (Jan 21, 2003)
- 8: 26199 (Jan 21, 2003)
- 9: 26199 (Jan 21, 2003)
- 10: Calculator Nerd 256 (Jan 28, 2003)
- 11: ITIWBS (Apr 15, 2015)

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