11.0453610171 or 11.0453610172

John E. Franklin · 2012-04-02 14:52:35

My calculator doesn't seem to know which number is closer to the
square root of 122. If someone has a calculation that is longer
than 12 digits, could you post the number to a few more digits
for me because I wrote a 1000 digit calculator but my virus
software put the compiler into quarantine a couple years ago
so I can't use it anymore.

MathsIsFun · 2012-04-02 18:25:21

11.0453610171872607742109138433443170608522796203345013271971025945627...

Bob · 2012-04-02 19:43:32

hi John,

Looks like you've been given your number, but I'll talk about the two issues you have raised.

Quarantined software: I had this problem with some software. Every time I tried to test the compiled file (.exe), Norton quarantined it. But there is a way you can 'tell' the virus checker that this file is OK. Took a while to find how to do it but once I had, I was able to use the software OK. You also should be able to rescue quarantined software and bring it back into the light.

Calculator accuracy: Calculators work to a greater accuracy than is shown in the display. They keep 'guard digits' in order to round the display to show the best accuracy possible. If you subtract the displayed digits from what's in the calculator's memory you will 'see' the difference and so can work out where your number lies in terms of rounding.

This has been an issue for calculator designers ever since they were invented ( the calculators not the designers ). In the 'early days' it was considered a good test to try things like TAN(ARCTAN(number)) to see if you got the same thing back. I stumbled across one interesting accuracy issue with an early PC. If I did INT(255.3 x 100) I got 25529 . I investigated in terms of the binary digits and revealed that the number of digits being used for this calculation meant a '1' was being lost down at place 40 (I think it was).

Of course, accuracy has improved a lot since those days, but it's useful to remember that calcs and computers are just shuffling binary digits according to some rule that may or may not work.

Bob

John E. Franklin · 2012-04-07 02:54:31

Thanks again to mf for the longer number. I appreciate it. I like to try to memorize numbers that end if 22 in the last week.

bbbndy: thanx for the interesting details you've seen and learned about digital calculations on our purchasable equipment.
Also, you see a long time ago when it quarantined my compiler or linker, it asked me should we delete it, and i said, yes, delete it thinking it had got a virus in it and was different. Now I need to find a new C compiler and linker someday that is preferably free, so I can port if needed any syntactical changes and get my 1000 to 10000 digit calculator working again.

Math Is Fun Forum

#1 2012-04-02 14:52:35

11.0453610171 or 11.0453610172

#2 2012-04-02 18:25:21

Re: 11.0453610171 or 11.0453610172

#3 2012-04-02 19:43:32

Re: 11.0453610171 or 11.0453610172

#4 2012-04-07 02:54:31

Re: 11.0453610171 or 11.0453610172

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