Thống kê Phân phối Tần suất của Chữ số 0 đến 9 trong Pi
Chúng tôi đã đếm số lần xuất hiện và tần suất của các chữ số từ 0 đến 9 trong 100 tỷ chữ số đầu tiên của pi. Chúng tôi nhận thấy rằng khi số chữ số của pi tăng, tần suất của chúng dần dần trở nên trung bình.
Trong 100 tỷ chữ số đầu tiên của pi, từ ít đến nhiều chữ số, chúng tôi đã ghi dữ liệu riêng về phân phối của 82 bộ số khác nhau. Số lần xuất hiện được liệt kê ở phía trên và tần suất được liệt kê ở phía dưới.
Bảng tần suất của mỗi chữ số trong 100 tỷ chữ số đầu tiên của Pi
| # | Chữ số | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 10 | 00.00% | 220.00% | 110.00% | 220.00% | 110.00% | 220.00% | 110.00% | 00.00% | 00.00% | 110.00% |
| 2 | 20 | 00.00% | 210.00% | 210.00% | 420.00% | 210.00% | 315.00% | 15.00% | 15.00% | 210.00% | 315.00% |
| 3 | 30 | 00.00% | 26.67% | 413.33% | 723.33% | 310.00% | 310.00% | 310.00% | 26.67% | 310.00% | 310.00% |
| 4 | 40 | 12.50% | 37.50% | 512.50% | 717.50% | 410.00% | 410.00% | 37.50% | 37.50% | 512.50% | 512.50% |
| 5 | 50 | 12.00% | 510.00% | 510.00% | 918.00% | 48.00% | 510.00% | 48.00% | 48.00% | 510.00% | 816.00% |
| 6 | 60 | 35.00% | 58.33% | 610.00% | 915.00% | 610.00% | 610.00% | 46.67% | 58.33% | 610.00% | 1016.67% |
| 7 | 70 | 45.71% | 68.57% | 710.00% | 1014.29% | 710.00% | 710.00% | 57.14% | 68.57% | 710.00% | 1115.71% |
| 8 | 80 | 67.50% | 67.50% | 911.25% | 1012.50% | 810.00% | 78.75% | 78.75% | 67.50% | 911.25% | 1215.00% |
| 9 | 90 | 77.78% | 66.67% | 1112.22% | 1112.22% | 910.00% | 77.78% | 88.89% | 66.67% | 1213.33% | 1314.44% |
| 10 | 100 | 88.00% | 88.00% | 1212.00% | 1212.00% | 1010.00% | 88.00% | 99.00% | 88.00% | 1212.00% | 1313.00% |
| 11 | 200 | 199.50% | 2010.00% | 2412.00% | 2010.00% | 2211.00% | 2010.00% | 157.50% | 126.00% | 2512.50% | 2311.50% |
| 12 | 300 | 268.67% | 3010.00% | 3511.67% | 3110.33% | 3712.33% | 279.00% | 3110.33% | 196.33% | 3411.33% | 3010.00% |
| 13 | 400 | 399.75% | 4310.75% | 4411.00% | 4010.00% | 4611.50% | 399.75% | 4210.50% | 246.00% | 4411.00% | 399.75% |
| 14 | 500 | 459.00% | 5911.80% | 5310.60% | 5110.20% | 5310.60% | 5010.00% | 489.60% | 367.20% | 5310.60% | 5210.40% |
| 15 | 600 | 549.00% | 6711.17% | 6310.50% | 6410.67% | 6410.67% | 559.17% | 6210.33% | 508.33% | 599.83% | 6210.33% |
| 16 | 700 | 649.14% | 7610.86% | 7510.71% | 7210.29% | 7310.43% | 669.43% | 7010.00% | 659.29% | 689.71% | 7110.14% |
| 17 | 800 | 749.25% | 9211.50% | 8310.38% | 8010.00% | 8010.00% | 739.13% | 779.63% | 759.38% | 769.50% | 9011.25% |
| 18 | 900 | 869.56% | 10311.44% | 9310.33% | 9410.44% | 899.89% | 849.33% | 859.44% | 839.22% | 889.78% | 9510.56% |
| 19 | 1,000 | 939.30% | 11611.60% | 10310.30% | 10310.30% | 939.30% | 979.70% | 949.40% | 959.50% | 10110.10% | 10510.50% |
| 20 | 2,000 | 1829.10% | 21210.60% | 20710.35% | 1899.45% | 1959.75% | 20510.25% | 20010.00% | 1979.85% | 20210.10% | 21110.55% |
| 21 | 3,000 | 2598.63% | 30810.27% | 30310.10% | 2668.87% | 31810.60% | 31510.50% | 30210.07% | 2879.57% | 31010.33% | 33211.07% |
| 22 | 4,000 | 3629.05% | 42910.73% | 40810.20% | 3699.23% | 40510.13% | 41710.43% | 3979.93% | 3779.43% | 40510.13% | 43110.78% |
| 23 | 5,000 | 4669.32% | 53110.62% | 4969.92% | 4609.20% | 50810.16% | 52510.50% | 51310.26% | 4889.76% | 4929.84% | 52110.42% |
| 24 | 6,000 | 5569.27% | 62610.43% | 5949.90% | 5739.55% | 61310.22% | 62210.37% | 61910.32% | 60610.10% | 5829.70% | 60910.15% |
| 25 | 7,000 | 6579.39% | 73310.47% | 6929.89% | 6879.81% | 70210.03% | 73010.43% | 70810.11% | 6939.90% | 6809.71% | 71810.26% |
| 26 | 8,000 | 7549.43% | 83310.41% | 81110.14% | 7829.78% | 80910.11% | 83410.43% | 81610.20% | 7859.81% | 7649.55% | 81210.15% |
| 27 | 9,000 | 8559.50% | 93610.40% | 91110.12% | 8859.83% | 91010.11% | 93210.36% | 91410.16% | 8839.81% | 8549.49% | 92010.22% |
| 28 | 10,000 | 9689.68% | 102610.26% | 102110.21% | 9759.75% | 101210.12% | 104610.46% | 102110.21% | 9709.70% | 9479.47% | 101410.14% |
| 29 | 20,000 | 19549.77% | 19979.99% | 19869.93% | 19879.94% | 204310.22% | 208210.41% | 201710.09% | 19539.77% | 19619.81% | 202010.10% |
| 30 | 30,000 | 29989.99% | 304810.16% | 28979.66% | 29799.93% | 305710.19% | 304910.16% | 301210.04% | 29749.91% | 29729.91% | 301410.05% |
| 31 | 40,000 | 39899.97% | 406010.15% | 38929.73% | 39729.93% | 401410.04% | 404010.10% | 402610.07% | 39779.94% | 403210.08% | 399810.00% |
| 32 | 50,000 | 503310.07% | 505410.11% | 48679.73% | 49489.90% | 501110.02% | 505210.10% | 501810.04% | 49779.95% | 503010.06% | 501010.02% |
| 33 | 60,000 | 600910.02% | 607110.12% | 58949.82% | 59769.96% | 59839.97% | 608610.14% | 59809.97% | 59959.99% | 601510.03% | 59919.99% |
| 34 | 70,000 | 69929.99% | 710610.15% | 68929.85% | 701810.03% | 69489.93% | 703310.05% | 69669.95% | 704710.07% | 701310.02% | 69859.98% |
| 35 | 80,000 | 79729.97% | 814110.18% | 79209.90% | 79769.97% | 79579.95% | 804410.06% | 802510.03% | 803110.04% | 79539.94% | 79819.98% |
| 36 | 90,000 | 89909.99% | 919310.21% | 88879.87% | 902010.02% | 89579.95% | 902610.03% | 89929.99% | 902810.03% | 89539.95% | 89549.95% |
| 37 | 100,000 | 999910.00% | 1013710.14% | 99089.91% | 1002610.03% | 99719.97% | 1002610.03% | 1002810.03% | 1002510.03% | 99789.98% | 99029.90% |
| 38 | 200,000 | 2010410.05% | 2006310.03% | 198929.95% | 2001110.01% | 198749.94% | 2019910.10% | 198989.95% | 2016310.08% | 199559.98% | 198419.92% |
| 39 | 300,000 | 3000110.00% | 3003410.01% | 298799.96% | 3013910.05% | 298449.95% | 3027210.09% | 298909.96% | 3022610.08% | 299269.98% | 297899.93% |
| 40 | 400,000 | 4001310.00% | 4006910.02% | 398139.95% | 4009810.02% | 4009310.02% | 4026110.07% | 398599.96% | 4027810.07% | 398149.95% | 397029.93% |
| 41 | 500,000 | 499159.98% | 4998410.00% | 497529.95% | 5000110.00% | 5035710.07% | 5023510.05% | 498249.96% | 5023010.05% | 499119.98% | 497919.96% |
| 42 | 600,000 | 6001910.00% | 598749.98% | 596279.94% | 6005110.01% | 6047510.08% | 6017710.03% | 597619.96% | 6014510.02% | 6001510.00% | 598569.98% |
| 43 | 700,000 | 7003710.01% | 698399.98% | 697969.97% | 6999410.00% | 7060110.09% | 7018010.03% | 695779.94% | 6997610.00% | 7013810.02% | 698629.98% |
| 44 | 800,000 | 799499.99% | 798519.98% | 798729.98% | 7996310.00% | 8044710.06% | 8029810.04% | 796509.96% | 798839.99% | 8016710.02% | 799209.99% |
| 45 | 900,000 | 8999510.00% | 897789.98% | 899129.99% | 9007010.01% | 9033010.04% | 9018010.02% | 895749.95% | 898659.99% | 9021410.02% | 9008210.01% |
| 46 | 1,000,000 | 9995910.00% | 997579.98% | 10002610.00% | 10023010.02% | 10023010.02% | 10035910.04% | 995489.95% | 998009.98% | 9998510.00% | 10010610.01% |
| 47 | 2,000,000 | 1997929.99% | 1995359.98% | 20007710.00% | 20014210.01% | 20008310.00% | 20052110.03% | 1994039.97% | 20031010.02% | 1994479.97% | 20069010.03% |
| 48 | 3,000,000 | 2994519.98% | 2996409.99% | 29986710.00% | 30031110.01% | 30023410.01% | 30034210.01% | 2994619.98% | 30065510.02% | 2994409.98% | 30059910.02% |
| 49 | 4,000,000 | 3994189.99% | 3994639.99% | 39982210.00% | 39991410.00% | 40079210.02% | 40003210.00% | 3990329.98% | 40065010.02% | 40018310.00% | 40069410.02% |
| 50 | 5,000,000 | 4996209.99% | 49989810.00% | 4995089.99% | 49993410.00% | 50054410.01% | 50002410.00% | 4987589.98% | 50088010.02% | 49988010.00% | 50095410.02% |
| 51 | 6,000,000 | 5994769.99% | 60034610.01% | 5996829.99% | 59997710.00% | 60035710.01% | 59976910.00% | 5984389.97% | 60077910.01% | 60025510.00% | 60092110.02% |
| 52 | 7,000,000 | 6993239.99% | 70045610.01% | 69994810.00% | 70033010.00% | 70026610.00% | 69983710.00% | 6984289.98% | 70041010.01% | 70055110.01% | 70045110.01% |
| 53 | 8,000,000 | 7991119.99% | 80011010.00% | 79978810.00% | 80023510.00% | 80020110.00% | 80015410.00% | 7988859.99% | 80056010.01% | 80063810.01% | 80031810.00% |
| 54 | 9,000,000 | 8988249.99% | 89991010.00% | 89996110.00% | 89982210.00% | 90094910.01% | 90063210.01% | 8992439.99% | 90044510.00% | 90020910.00% | 90000510.00% |
| 55 | 10,000,000 | 9994409.99% | 9993339.99% | 100030610.00% | 99996510.00% | 100109310.01% | 100046610.00% | 9993379.99% | 100020610.00% | 99981410.00% | 100004010.00% |
| 56 | 20,000,000 | 200116210.01% | 199983210.00% | 200140910.01% | 199934410.00% | 200110510.01% | 200012510.00% | 199926910.00% | 19984049.99% | 199972010.00% | 199963010.00% |
| 57 | 30,000,000 | 299915710.00% | 300055310.00% | 300096910.00% | 299922310.00% | 300259310.01% | 299999710.00% | 299954810.00% | 29981759.99% | 299959210.00% | 300019310.00% |
| 58 | 40,000,000 | 399862010.00% | 400068910.00% | 400175410.00% | 399904610.00% | 400229710.01% | 400067810.00% | 399880410.00% | 399868510.00% | 399871110.00% | 400071610.00% |
| 59 | 50,000,000 | 499963210.00% | 500222010.00% | 500057310.00% | 499863110.00% | 500400810.01% | 499979710.00% | 499801710.00% | 499889510.00% | 499849410.00% | 499973310.00% |
| 60 | 60,000,000 | 600098910.00% | 600295710.00% | 600049610.00% | 599806610.00% | 600357310.01% | 599845410.00% | 599777610.00% | 599849910.00% | 599966610.00% | 599952410.00% |
| 61 | 70,000,000 | 699875210.00% | 700422910.01% | 700075510.00% | 699958210.00% | 700296210.00% | 699686210.00% | 699793310.00% | 699851410.00% | 700096510.00% | 699944610.00% |
| 62 | 80,000,000 | 799880710.00% | 800278810.00% | 800182710.00% | 799765710.00% | 800352510.00% | 799650010.00% | 799816510.00% | 799938910.00% | 800030810.00% | 800103410.00% |
| 63 | 90,000,000 | 899906110.00% | 900229910.00% | 900183210.00% | 899911510.00% | 900443710.00% | 89948369.99% | 899890210.00% | 899896310.00% | 900094710.00% | 899960810.00% |
| 64 | 100,000,000 | 999992210.00% | 1000247510.00% | 1000109110.00% | 999844310.00% | 1000386310.00% | 99934789.99% | 999941710.00% | 999961010.00% | 1000218010.00% | 999952110.00% |
| 65 | 200,000,000 | 1999743710.00% | 2000377410.00% | 2000218510.00% | 2000141110.00% | 1999984610.00% | 1999303110.00% | 1999916110.00% | 2000028710.00% | 2000230710.00% | 2000056110.00% |
| 66 | 300,000,000 | 2999835610.00% | 3000058210.00% | 3000633710.00% | 2999986810.00% | 2999981010.00% | 2999309910.00% | 2999891310.00% | 2999907110.00% | 3000368210.00% | 3000028210.00% |
| 67 | 400,000,000 | 3999604810.00% | 3999737510.00% | 4001179110.00% | 3999503010.00% | 4000101410.00% | 3999212310.00% | 4000189910.00% | 4000031410.00% | 4000573510.00% | 3999867110.00% |
| 68 | 500,000,000 | 4999527910.00% | 5000043710.00% | 5001143610.00% | 4999241010.00% | 5000512110.00% | 4999067810.00% | 4999882010.00% | 5000031910.00% | 5000663210.00% | 4999886810.00% |
| 69 | 600,000,000 | 5999172510.00% | 5999759710.00% | 6000859110.00% | 5999255910.00% | 6000799010.00% | 5999021110.00% | 6000389510.00% | 5999877210.00% | 6001095810.00% | 5999770210.00% |
| 70 | 700,000,000 | 6998989110.00% | 6999775510.00% | 7000649710.00% | 6999402910.00% | 7000958110.00% | 6999453610.00% | 7000379510.00% | 6999701410.00% | 7000516110.00% | 7000174110.00% |
| 71 | 800,000,000 | 7999189710.00% | 7999700310.00% | 8000331610.00% | 7998965210.00% | 8001607310.00% | 7999612010.00% | 8000414810.00% | 7999510910.00% | 8000293210.00% | 8000375010.00% |
| 72 | 900,000,000 | 8999120810.00% | 8999838110.00% | 9000096810.00% | 8999008410.00% | 9001313210.00% | 8999608610.00% | 9000641210.00% | 8999565810.00% | 9000197910.00% | 9000609210.00% |
| 73 | 1,000,000,000 | 9999394210.00% | 9999733410.00% | 10000241010.00% | 9998691210.00% | 10001195810.00% | 9999888510.00% | 10001038710.00% | 9999606110.00% | 10000183910.00% | 10000027210.00% |
| 74 | 2,000,000,000 | 19999431610.00% | 19999528410.00% | 19999257510.00% | 19999947110.00% | 20001436810.00% | 19998985210.00% | 20000478510.00% | 19997929310.00% | 20001784410.00% | 20001221210.00% |
| 75 | 3,000,000,000 | 29999914310.00% | 29999593210.00% | 29998912610.00% | 29999229110.00% | 30000225710.00% | 29997901610.00% | 30002544710.00% | 29997551010.00% | 30001654910.00% | 30002472910.00% |
| 76 | 4,000,000,000 | 40000123310.00% | 40000228510.00% | 39996540510.00% | 39998447010.00% | 40000693610.00% | 39998905210.00% | 40003303410.00% | 39999612210.00% | 40000474110.00% | 40001672210.00% |
| 77 | 5,000,000,000 | 49998900110.00% | 50003412710.00% | 49998494910.00% | 49999032210.00% | 49997828410.00% | 49999535210.00% | 50001981810.00% | 50000170210.00% | 49999052210.00% | 50001592310.00% |
| 78 | 6,000,000,000 | 59996300510.00% | 60003326010.00% | 59999916910.00% | 60000024410.00% | 59995743910.00% | 60001717610.00% | 60001658810.00% | 60000904310.00% | 59998703810.00% | 60001703810.00% |
| 79 | 7,000,000,000 | 69997157910.00% | 70003228710.00% | 70001446210.00% | 69999086510.00% | 69995649110.00% | 70000709510.00% | 70000146010.00% | 70000794310.00% | 69999152210.00% | 70002629610.00% |
| 80 | 8,000,000,000 | 79995983910.00% | 80003117210.00% | 80001683410.00% | 79998588710.00% | 79994299110.00% | 79999530210.00% | 80000338310.00% | 80001274510.00% | 80001122910.00% | 80004061810.00% |
| 81 | 9,000,000,000 | 89995781310.00% | 90003037510.00% | 90001614110.00% | 89999275310.00% | 89994181010.00% | 89999775010.00% | 90000218310.00% | 90002338110.00% | 89999171810.00% | 90004607610.00% |
| 82 | 10,000,000,000 | 99996799410.00% | 100003779010.00% | 100001727110.00% | 99997648410.00% | 99993768810.00% | 100000792810.00% | 99998573110.00% | 100004133010.00% | 99999177210.00% | 100003601210.00% |
Phân phối chữ số trong Pi
Sau khi đếm số lần xuất hiện của các chữ số từ 0 đến 9 trong 100 tỷ chữ số đầu tiên của pi, chúng ta có thể dễ dàng phát hiện rằng các chữ số của pi được phân phối ngẫu nhiên và đồng đều. Tần suất của các chữ số từ 0 đến 9 là bằng nhau.
Nguồn Dữ liệu Pi
Chúng tôi cung cấp tải xuống 100 tỷ chữ số đầu tiên của pi. Bạn có thể tải xuống dữ liệu pi từ trang tải xuống và phân tích hoặc biên soạn dữ liệu tự mình.