Value of 'pi' using calculator is 3.141592654.A substitute for 'pi' is 22/7.But its value is 3.142857.Why so?

Answer 1

Regardless of David La Pierre's opinion, you don't have to be ignorant to use 22/7 for pi. It's actually quite a good approximation, and often very convenient.

If, on your geometry worksheet, they tell you the diameter of a large key ring is 7 cm., and ask you for the circumference, the best answer is 7 times pi, or 7 times 22/7, or 22 cm. Anybody who gets out their calculator and says the circumference is 21.991149 cm. needs to get head examined.

It's already been pointed out that pi is an irrational number that just keeps going on forever and ever, and that any fraction (rational number) is, at best, an approximation.

The reason they use 22/7 is that it's convenient, and it's pretty good. As you point out, the calculator value for pi is 3.141592654 (and by fussing some, you can get more decimal digits if you wish), and the value of 22/7 is 3.142857143. If you subtract the two, the difference is 0.001264489, and 22/7 is only off by 0.04% (that's 4 parts in 10,000).

It's not hard to get better fractional approximations for pi. I just fussed around with my calculator, and got this: 355/113. When you divide that one out, you get 3.14159292 (exact, with no truncation or rounding). This is accurate to within 0.000000266, or 0.0000085% (error of less than one part in 10 million).

(And Sherman81 said you can't do what we just did -- to get a fraction that approximates pi better than 22/7.)

So 355/113 is a better approximation of pi than 22/7. But which one is easier to remember and use?

I guess that answers your question.

Answer 2

Hi:

To answer your question you need to know what pi is : It is the ratio of a circle's circumference to it's diameter. it a constant number that never changes no matter how big or small the diameter of the circle you make. Start by cutting some paper circles of varying diameters say 1 inch , 2 inch and 3 inch take a ruler and mark a spot on the edge of the paper circle and position that spot on the zero mark on the ruler. Then carefully roll the paper circle along the ruler and see where you end up as that point return to the bottom of the circle . This is the circumference now divide that number by the circle diameter, you should get a close value for pi. of about 3.1 or 3.2

Now to answer the second part of your question.
Back about three thousand years ago the ancient Egyptians estimated Pi to be about 3 units (you have to remember that their Mathematics were quite primitive and they had no algebra to help them at this time). Later the ancient Greeks developed and used the area of triangles filling a circle method to estimate pi to be between 22/7 and 3 10/71

{pi= sin ( (360/N)/2)*N

pi = tan(360/N)/2)*N { N= the number of triangles try the numbers between 100,000 to 1*10^50) for good results}

This is the modern day formula for the filling the circle method used by the Greek }

around 240 B.C. However this was good enough for building things and such, but is was not good enough for mathematicans however. So a quest was started to find the true value for pi and various mehods were used to get a better and better estimate for the value of pi. In about the 15th and 16 th centry A.D. Various discovery where made about Pi:

1) Pi is irrational { Meaning it does not repeat itself ever ; like 1/3} and it's transcendental { Meaning that powers of and combination of powers of pi will not give finite whole numbers } So all formulae for computing pi will be infinitely long.

2) with the devolpment of Algbera and Calculus, certain series were found to give the approximate value of pi

Pi= sqr ( 6*(1 + 1/(2^2)+ 1/(3^2)+ 1/ (4^2) + 1/(5^2).....) { sqr means Square root}

or

Pi = 4*( 1- (1/3)+(1/5)-(1/7)+(1/9)- (1/11)......)

Those series take a long time to come to the value of Pi that we know Pi to be today. Which bring us to our era, when electronic computers where built, and as soon as they became avialable. Mathematican were able to confirm those series to be the appoximate value of Pi , which are still in use today. it has been calulated the about 15 billion decimal places and is so well known that it is use to gauged the speed and power of all supercomputers and computers that made today and in the future to come. and it being surpassed in the number of decimal places to be counted in. and it pop up in some interesting places.

Here Pi to a few hundred decimal places I got off the Internet:

3.

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9759556808 5683629725 3867913275 0555425244 9194358912

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7399482506 0739495073 5031690197 3185211955 2635632584
3390998224 9862406703 1076831844 6607291248 7475403161

7969941139 7387765899 8685541703 1884778867 5929026070
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5355570464 6349113208 5918979613 2791319756 4909760001
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9144051099 4235883034 5463534923 4982688362 4043327267
4155403016 1950568065 4180939409 9820206099 9414021689

0900708213 3072308966 2119775530 6659188141 1915778362
7292746156 1857103721 7247100952 1423696483 0864102592
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3746501402 6278240273 4696252821 7174941582 3317492396
8353013617 8653673760 6421667781 3773995100 6589528877

4276626368 4183068019 0804609849 8094697636 6733566228
2915132352 7888061577 6827815958 8669180238 9403330764
4191240341 2022316368 5778603572 7694154177 8826435238
1319050280 8701857504 7046312933 3537572853 8660588890
4583111450 7739429352 0199432197 1171642235 0056440429
7989208159 4307167019 8574692738 4865383343 6145794634
1759225738 9858800169 8014757420 5429958012 4295810545
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6607915874 3698654122 2348341887 7229294463 3517865385
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7771689348 4917660771 7052771876 0119990814 4113058645
5779105256 8430481144 0261938402 3224709392 4980293355
0731845890 3553971330 8844617410 7959162511 7148648744
6861124760 5428673436 7090466784 6867027409 1881014249
7111496578 1772427934 7070216688 2956108777 9440504843
7528443375 1088282647 7197854000 6509704033 0218625561
4733211777 1174413350 2816088403 5178145254 1964320309
5760186946 4908868154 5285621346 9883554445 6024955666
8436602922 1951248309 1060537720 1980218310 1032704178

3866544718 1260397190 6884623708 5751808003 5327047185
6594994761 2424811099 9288679158 9690495639 4762460842
4065930948 6215076903 1498702067 3533848349 5508363660
1784877106 0809804269 2471324100 0946401437 3603265645
1845667924 5666955100 1502298330 7984960799 4988249706
1723674493 6122622296 1790814311 4146609412 3415935930
9585407913 9087208322 7335495720 8075716517 1876599449
8569379562 3875551617 5754380917 8052802946 4200447215
3962807463 6021132942 5591600257 0735628126 3873310600
5891065245 7080244749 3754318414 9401482119 9962764531
0680066311 8382376163 9663180931 4446712986 1552759820
1451410275 6006892975 0246304017 3514891945 7636078935
2855505317 3314164570 5049964438 9093630843 8744847839
6168405184 5273288403 2345202470 5685164657 1647713932
3775517294 7951261323 9822960239 4548579754 5865174587
8771331813 8752959809 4121742273 0035229650 8089177705
0682592488 2232215493 8048371454 7816472139 7682096332
0508305647 9204820859 2047549985 7320388876 3916019952
4091893894 5576768749 7308569559 5801065952 6503036266
1597506622 2508406742 8898265907 5106375635 6996821151

0949669744 5805472886 9363102036 7823250182 3237084597
9011154847 2087618212 4778132663 3041207621 6587312970
8112307581 5982124863 9807212407 8688781145 0165582513
6178903070 8608701989 7588980745 6643955157 4153631931
9198107057 5336633738 0382721527 9884935039 7480015890
5194208797 1130805123 3933221903 4662499171 6915094854
1401871060 3546037946 4337900589 0957721180 8044657439
6280618671 7861017156 7409676620 8029576657 7051291209
9079443046 3289294730 6159510430 9022214393 7184956063
4056189342 5130572682 9146578329 3340524635 0289291754
7087256484 2600349629 6116541382 3007731332 7298305001
6025672401 4185152041 8907011542 8857992081 2198449315
6999059182 0118197335 0012618772 8036812481 9958770702
0753240636 1259313438 5955425477 8196114293 5163561223
4966615226 1473539967 4051584998 6035529533 2924575238
8810136202 3476246690 5581643896 7863097627 3655047243
4864307121 8494373485 3006063876 4456627218 6661701238
1277156213 7974614986 1328744117 7145524447 0899714452
2885662942 4402301847 9120547849 8574521634 6964489738
9206240194 3518310088 2834802492 4908540307 7863875165

9113028739 5878709810 0772718271 8745290139 7283661484
2142871705 5317965430 7650453432 4600536361 4726181809
6997693348 6264077435 1999286863 2383508875 6683595097
2655748154 3194019557 6850437248 0010204137 4983187225
9677387154 9583997184 4490727914 1965845930 0839426370
2087563539 8216962055 3248032122 6749891140 2678528599
6734052420 3109179789 9905718821 9493913207 5343170798
0023736590 9853755202 3891164346 7185582906 8537118979
5262623449 2483392496 3424497146 5684659124 8918556629
5893299090 3523923333 3647435203 7077010108 4388003290
7598342170 1855422838 6161721041 7603011645 9187805393
6744747205 9985023582 8918336929 2233732399 9480437108
4196594731 6265482574 8099482509 9918330069 7656936715
9689364493 3488647442 1350084070 0660883597 2350395323
4017958255 7036016936 9909886711 3210979889 7070517280
7558551912 6993067309 9250704070 2455685077 8679069476
6126298082 2516331363 9952117098 4528092630 3759224267
4257559989 2892783704 7444521893 6320348941 5521044597
2618838003 0067761793 1381399162 0580627016 5102445886
9247649246 8919246121 2531027573 1390840470 0071435613

6231699237 1694848132 5542009145 3041037135 4532966206
3921054798 2439212517 2540132314 9027405858 9206321758
9494345489 0684639931 3757091034 6332714153 1622328055
2297297953 8018801628 5907357295 5416278867 6498274186
1642187898 8574107164 9069191851 1628152854 8679417363
8906653885 7642291583 4250067361 2453849160 6741373401

Check the Sources

Answer 3

Actually, you have answered your own question. 22/7 is a "substitute" for pi. A substitute, in any manner, is not and will never be the same as the original. That's why we use the term "substitute". A "substitute" may never be called a "substitute" if it is one and the same as the original.

Prior to hand held calculators, if we were asked to give the value of pi within (lets say) 20 decimal places (my exaggeration), no one could give an answer quickly and accurately without dividing 22 by 7 (because most of us memorized only the digits 3.1416).

Now, all we have to do is punch the "pi" symbol and we get exactly what we want.

On a lighter side please note that no one perished or died using 22/7 instead of "pi" unless 22/7 is a giant billboard that fell on someone while pondering the difference between "pi" and 22/7. He. He. He.

**bpiguy wrote that if you use 355/113 you'll get an exact number without truncation is not exactly right. If you use your pc's calculator, you still come up with an infinite number (my pc gives me 31 decimal places).

Answer 4

back before the advent of the calculator (ugh I'm aging myself) the easiest fracton that came close to pi was 22/7 and the fraction really hasn't been replaced.

interesting note. even the caculator value is non-real function for pi...

pi is a value that the place values go on and on forever to the right

Answer 5

22/7 isn't the precise value of pi, people use 22/7 as the fraction for pi because its the closest fraction value that ANYONE has ever come up with that comes closest to the value of pi.

If you divide pi by (22/7), you get about .9995976625058...

and no one else has come up with a different fraction that comes close to it.

Answer 6

22/7 is just an approximation to pi. Neither of those numbers is equal to pi (which is irrational, so can't be represented by a fraction or a decimal), but the one in your calculator is closer.

Answer 7

The 'real' value of pi is 22/7 . Your calculator makes the number round because it's capacity is not big enough to show the exact value.

For example let's say your calculator can show 4 decimals and the real result of the calculation is '1,33468' , it will show you the number as 1,3347. It is just like that.

Answer 8

Only ignorant people use 22/7 in my opinion :-)

*edit*
"people use 22/7 as the fraction for pi because its the closest fraction value that ANYONE has ever come up with that comes closest to the value of pi."
Hahahahahahahahahaha.... how about 3,141,592,654/1,000,000,000?
Ooo, I must be a genius or something!

Answer 9

the value of 22/7 is close enough for practical calculations. If you are still not satisfied, you could use 355/113 which is much more accurate.

Answer 10

because you dont need exact values for pi

usually when your using pi it is set to equal 3.14 that gives you a good estimate of what the actual answer is

also the second pi number is basically rounded up a few decimal places