The calculator is wrong. ?

Question

We all know pi is equal to 3.14159265358979... however it only shows 3.141592654 on most calculators, it has been rounded to 4 because the next number is a 5. When you press the pi button then minus, for example 3 you would expect to get the answer 0.141592654, again the last digit being rounded up. However you get 0.141592653, notice the last digit.
Is there any mathematical reason for this?

Answer 1

I don't know. I know that the peculiar rounding results are because of the way the calculator circuitry is designed. But this one is an oddie. By rights, since the digits down at the end of the display read 3.14...65358..., it should round off to 654.



I checked my TI-36 and after subtracting 3, and multiplying by 1000, I got 14.15926536, which is correct.

Answer 2

It depends on the programming in the calculator. Sometimes the number will be rounded up when the digit behind it is a five, like we were taught in grade school, but sometimes it just gets truncated (rounded down/stays the same) when it is a five. As for the last digit when subtracting it is the same answer as before, sometimes it gets truncated and sometimes it gets rounded. If there are only so many digits stored in the calculator for π it will only calculate to that digit, and usually the last digit will be off when doing this. It is because of how the calculator estimates numbers.



Don't worry about it because the chances of that 0.000000001 unit mattering are very low.

Answer 3

When a small processor goes to crunch a math problem, it usually can't use decimal points, so it uses a certain number of digits, usually 10. However it may be limited by the number of digits after the decimal point it can display.

So when you find pi, it is 3.141 592 654 or ten digits. Pi - 3 is .1415926536 in the processor, which is also ten digits. But when it goes to display it. is always puts a zero in front, so it displays 0.1415926536, but the last digit won't fit in the display or display memory, so it simply chops it off.

My calculator, a Sharp EL-W516 will also do this when it is in float mode, but when I fix it to 9 decimal places, or change it to scientific or engineering mode, then it displays pi-3 correctly. My TI-89 does not do this, so it might also depend on the calculator as well.

Answer 4

Hi:



Some scientific calculators display only eight digits so the programmers made it to rounded it off to 8 decimal places. However there is a Thing called a buffer or a section in the scientific calculator Rom memory that hold the value of pi which hold a extra digit for pi. the Newer more advanced scientific calculators like the TI -80 series can display more digits and has more memory to hold it; so it can display it depend on how you set the rounding ( or set the number of digits you want the calculator to display) up value too.



but here some info I've found on pi :



3 + 4/28 - 1/(790 + 5/6) appox = PI



π = 3927/1250 = 3.1416



π ≈ 62832⁄20000



pi = 22/7 and pi 355/113



31 ^ (1/3)



54648/17395 accurate to 7 decimal places



(2143/22)^.25 or (97 9/22)^ (1/4) accurate to 9 decimal places



833009/ 265155 = pi to 10 decimal places



52163/16604 pi is accurate to the true value to six or seven decimal places



Pi= aprox= 3.1415926535897932846264



ln(640320^3 + 744) / v163



A more accurate faction value for is : 104348 / 33215



first fraction found for pi is between 22/7 and 3 10/71



5419351 / 1725033 = pi



pi appox = 355/113



144029661/45846065



69305155/22060516



5419351/1725033



312689/99532



3 + 4/28 - 1/(790 + 5/6) appox PI



A way to remember pi



How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics. All of thy geometry, Herr Planck, is fairly hard...:



Sir, I send a rhyme excelling

In sacred truth and rigid spelling

Numerical sprites elucidate

For me the lexicon's full weightt.





Sir, I bear a rhyme excelling

In mystic force and magic spelling





3.1415926535897932846264



Fourth root of (97+9/22) = 3.14159265



52,163/16,604 = 3.1415923873765357745121657431944



instresting things about Pi



American Pi :



in the Hebrew Bible we do see

the Circle Ratio appears as three

and the Rhind Papyrus does Report four-thirds to the fourth.



website for Pi:





http://en.wikipedia.org/wiki/Pi



http://mathforum.org/isaac/problems/pi1....



http://www.joyofpi.com/



http://www.joyofpi.com/pilinks.html



http://3.1415926535897932384626433832795...



http://wasi.org/PI/pi_club.html



http://mathworld.wolfram.com/PiFormulas....



http://mathforum.org/library/drmath/view...



3.141592653589793238462643383279502884...



http://www.gutenberg.org/dirs/etext93/pi...



http://news.inq7.net/breaking/index.php?...



www.numbers.computation.free.fr/Const...



www.joyofpi.com/pifacts.html



www.cacr.caltech.edu/~roy/upi/pi....



www.yahoo.com/Science/Mathematics...



www.//oldweb.cecm.sfu.ca/personal/jborw...



www.cs.uwaterloo.ca/~alopez-o/mat...



www.eveandersson.com/pi/





newton.ex.ac.uk/research/qsystems...



www.maa.org/mathland/mathland_3_1...



www.math.hmc.edu/funfacts/ffiles/20010...



www.angio.net/pi/piquery



pi.nersc.gov



www.lrz-muenchen.de/~hr/numb/pi-irr.html



PBS.org - Nova Website - Look for the show entitled "Infinite Secrets"- Explain how Archimedes appoximated the value of pi along with a formula for the pi value



Books:





1. P. Beckmann, A History of p, St. Martin's Press, 1971; MR 56 #8261.



2. J. M. Borwein and P. B. Borwein, Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity, Wiley, 1987, pp. 46-52, 169-177, 337-362, 385-386; MR 99h:11147.



3. E. F. Assmus, Pi, Amer. Math. Monthly 92 (1985) 213-214.

T. Wayman, Discovering Archimedes' method for p, Mathcad file wayman.mcd, substantial revision by S. Finch.



4. G. M. Phillips, Archimedes and the complex plane, Amer. Math. Monthly 91 (1984) 108-114; MR 85h:40003.



5. G. Miel, Of calculations past and present: the Archimedean algorithm, Amer. Math. Monthly 90 (1983) 17-35; MR 85a:01006.



6. H. Dörrie, 100 Great Problems of Elementary Mathematics: Their History and Solution, Dover, 1965; MR 84b:00001.



7. E. Waymire, Buffon Noodles, Amer. Math. Monthly 101 (1994) 550-559; addendum 101 (1994) 791; MR 95g:60021a and MR 95g:60021b.



8. E. Wegert and L. N. Trefethen, From the Buffon needle problem to the Kreiss matrix theorem, Amer. Math. Monthly 101 (1994) 132-139; preprint; MR 95b:30036.



9. G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford, 1985; MR 81i:10002.



10. A. E. Taylor and R. Mann, Advanced Calculus, 2nd ed., Wiley, 1972; MR 83m:26001.



11. R. D. Carmichael and E. R. Smith, Mathematical Tables and Formulas, Dover, 1931.



12. M. R. Spiegel, Advanced Calculus, McGraw-Hill, 1968.



13. J. M. Borwein, P. B. Borwein and D. H. Bailey, Ramanujan, modular equations, and approximations to pi, or how to compute one billion digits of pi, Amer. Math. Monthly 96 (1989) 201-219; Organic Mathematics, ed. J. Borwein, P. Borwein, L. Jörgenson and R. Corless, Amer. Math. Soc., 1997, pp. 35-71; MR 90d:11143.



14. G. Almkvist and B. Berndt, Gauss, Landen, Ramanujan, the Arithmetic-Geo

Answer 5

It is still the number.

because there is no longer a 3 in front this leaves a vacant spot, it is 3 because afterwards there is a 6, therefore there is no need to round the 3 up to a 4.

on my ti-84 i get

pi = 3.1415926254

pi-3= .1415926536

the 4 changes to 36

Answer 6

Rounding.

Answer 7

its the precision of the calculator



as all Numeric calculations have to have a finite and terminating value



ie 12 digits



the two conditions are a source of discrepancet