The reciprocal of a number is 1 divided by the number. By using reciprocals, division is changed into multiplication, since a/b=a/b=ax1/b. The table gives the reciprocals of all numbers expressed with three significant figures to six significant figures. By proceeding in a manner similar to that just described for powers and roots, the reciprocal of any number correct to five significant figures may be obtained. The decimal point in the result may be located as follows: If the given number has an integral part, the number of ciphers following the decimal point in the reciprocal will be one less than the number of figures in the integral part of the given number; and if the given number is entirely decimal, the number of figures in the integral part of the reciprocal will be one greater than the number of ciphers following the decimal point in the given number. For example, the reciprocal of 3370 = .000296736 and of .00348 = 287.356.

When the number whose reciprocal is desired contains more than three significant figures, express the number to six significant figures (adding ciphers, if necessary, to make six figures) and find between what two numbers in the column headed - the significant figures of the given number falls; then proceed exactly as previously described to deter mine the fourth and fifth figures.

### Example

(a) The reciprocal of 379.426 =? (b)1/.0004692 =?

### Solution

(a) .379426 falls between .378788 = 1/2.64 and

.380228 = 1/2.63. The first difference is 380228 - 378788 = 1440: the second difference is 380228 - 379426 = 802; 802 -4- 1440 = .557, or .56. Hence, the first five significant figures are 26356, and the reciprocal of 379.426 is .0026356, to five significant figures.

(b) .469200 falls between .469484=1 / 2.13 and .467290=1 / 2.14

The first difference is 2194; the second difference is 284; 284/

2194 = .129+, or .13. Hence, 1/.0004692 = 2131.3, correct to five significant figures.

 n n2 n3 √n 1/n 1.01 1.0201 1 03030 1.00499 3.17805 1.00332 2.16159 4.65701 .990099 1.02 1.0404 1.06121 1.00995 3.19374 1.00662 2.16870 4.67233 .980392 1.03 1.0609 1.09273 1.01489 3.20936 1.00990 2.17577 4.68755 .970874 1.04 1.0816 1.12486 1.01980 3.22490 1.01316 2.18278 4.70267 .961539 1.05 1.1025 1.15763 1.02470 3.24037 1.01640 2.18976 4.71769 .952381 1.06 1.1236 1.19102 1.02956 3.25576 1.01961 2.19669 4.73262 .943396 1.07 1 1449 1.22504 1.03441 3.27109 1.02281 2.20358 4.74746 .934579 1.08 1.1664 1.25971 1.03923 3.28634 1.02599 2.21042 4.76220 .925926 1.09 1.1881 1.29503 1.04403 3.30151 1.02914 2.21722 4.77686 .917431 1.10 1.2100 1.33100 1.04881 3.31662 1.03228 2.22398 4.79142 .909091 1.11 1.2321 1 36763 1.05357 3.33167 1.03540 2.23070 4.80590 .900901 1.12 1.2544 1.40493 1.05830 3.34664 1.03850 2.23738 4.82028 .892857 1.13 1.2769 1.44290 1.06301 3.36155 1.04158 2.24402 4.83459 .884956 1.14 1.2996 1.48154 1.06771 3.37639 1.04464 2.25062 4.84881 .877193 1.15 1.3225 1.52088 1.07238 3.39116 1.04769 2.25718 4.86294 .869565 1.16 1.3456 1.56090 1.07703 3.40588 1.05072 2.26370 4.87700 .862069 1.17 1.3689 1.60161 1.08167 3.42053 1.05373 2.27019 4.89097 .854701 1.18 1.3924 1.64303 1.08628 3.43511 1.05672 2.27664 4.90487 .847458 1.19 1.4161 1.68516 1.09087 3.44964 1.05970 2.28305 4.91868 .840336 1.20 1.4400 1.72800 1.09545 3.46410 1.06266 2.28943 4.93242 .833333 1.21 1.4641 1.77156 1.10000 3.47851 1.06560 2.29577 4.94609 .826446 1.22 1.4884 1.81585 1.10454 3.49285 1.06853 2.30208 4.95968 .819672 1.23 1.5129 1.86087 1.10905 3.50714 1.07144 2.30835 4.97319 .813008 1.24 1.5376 1.90662 1.11355 3.52136 1.07434 2.31459 4.98663 .806452 1.25 1.5625 1.95313 1.11803 3.53553 .1.07722 2.32080 5.00000 .800000 1.26 1.5876 2.00038 1.12250 3.54965 1.08008 2.32697 5.01330 .793651 1.27 1.6129 2.04838 1.12694 3.56371 1.08293 2.33310 5.02653 .787402 1.28 1.6384 2.09715 1.13137 3.57771 1.08577 2.33921 5.03968 .781250 1.29 1.6641 2.14669 1.13578 3.59166 1.08859 2.34529 5.05277 .775194 1.30 1.6900 2.19700 1.14018 3.60555 1.09139 2.35134 5.06580 .769231 1.31 1.7161 2.24809 1.14455 3.61939 1.09418 2.35735 5.07875 .763359 1.32 1.7424 2.29997 1.14891 3.63318 1.09696 2.36333 5.09164 .757576 1.33 1.7689 2.35264 1.15326 3.64692 1.09972 2.36928 5.10447 .751880 1.34 1.7956 2.40610 1.15758 3.66060 1.10247 2.37521 5.11723 .746269 1.35 1.8225 2.46038 1.16190 3.67423 1.10521 2.38110 5.12993 .740741 1.36 1.8496 2.51546 1.16619 3.68782 1.10793 2.38696 5.14256 .735294 1.37 1.8769 2.57135 1.17047 3.70135 1.11064 2.39280 5.15514 .729927 1.88 1.9044 2.62807 1.17473 3.71484 1.11334 2.39861 5.16765 .724638 1.39 1.9321 2.68562 1.17898 3.72827 1.11602 2.40439 5.18010 .719425 1.40 1.9600 2.74400 1.18322 3.74166 1.11869 2.41014 5.19249 .714286 1.41 1.9881 2.80322 1.18743 3.75500 1.12135 2.41587 5.20483 .709220 1.42 2.0164 2.86329 1.19164 3.76829 1.12399 2.42156 521710 .704225 1.43 2.0449 2.92421 1.19583 3.78153 1.12662 2.42724 5.22932 .699301 1.44 2.0736 2.98598 1.20000 3.79473 1.12924 2.43288 5.24148 .694444 1.45 2.1025 3.04863 1.20416 3.80789 1.13185 2.43850 5.25359 .689655 1.46 | 2.1316 3.11214 1.20830 3.82099 1.13445 2.44409 5.26564 .684932 1.47 2.1609 3.17652 1.21244 3.83406 1.13703 2.44966 5.27763 .680272 1.48 2.1904 3.24179 1.21655 3.84708 1.13960 2.45520 5.28957 .675676 1.49 2.2201 3.30795 1.22066 3.86005 1.14216 2.46072 5.30146 .671141 1.50 2.2500 3.37500 1.22474 3.87298 1.14471 2.46621 5.31329 .666667
 n n2 n3 1/n 1.51 2.2801 3.44295 1.22882 3.88587 1.14725 2.47168 5.32507 .662252 1.52 2.3104 3.51181 1.23288 3.89872 1.14978 2.47713 5.33680 .667895 1.53 14400 3.58158 1.23693 3.91152 1.15230 2.48255 5.34848 .653595 1.54 2.3716 3.65226 1.24097 3.92428 1.15480 2.48794 5.36011 .649351 1.55 2.4025 3.72388 1.24499 3.93700 1.15729 2.49332 5.37169 .645161 1.56 2.4336 3.79642 1.24900 3.94968 1.15978 2.49866 5.38321 .641026 1.57 2.4649 3.86989 1.25300 3.96232 1.16225 2.50399 5.39469 .636943 1.58 2.4964 3.94431 1.25698 3.97492 1.16471 2.50930 5.40612 .632911 1.59 2.5281 4.01968 1.26095 3.98748 1.16717 2.51458 5.41750 .628931 1.60 2.5600 4.09600 1.26491 4.00000 1.16961 2.51984 5.42884 .625000 1.61 2.5921 4.17328 140080 4.01248 1.17204 2.52508 5.44012 .621118 1.62 2.6244 4.25153 1.97170 4.02492 1.17446 2.53030 5.45136 .617284 1.68 2•6569 4.33075 1.27671 4.03733 1.17687 2.53549 5.46256 .613497 1.64 2.6896 4.41094 1.28062 4.04969 1.17927 2.54067 5.47370 .609756 1.65 2.7225 4.49213 1.28452 4.06202 1.18167 2.54582 5.48481 .606061 1.66 2.7556 4.57430 140043 4.07431 1.18405 2.55095 5. 49586 .602410 1.67 2.7889 4.65746 1.29228 4.08656 1.18642 2.55607 5.50688 .598802 1.68 2.8224 4.74163 1.29615 4.09878 1.18878 2.56116 5.51785 .595238 1.69 2.8561 4.82681 1.30000 4.11096 1.19114 2.56623 5.52877 .591716 1.70 2.8900 4.91300 1.30384 4.12311 1.19348 2.57128 640000 .588235 1.71 2.9241 5.00021 1.30767 4.13521 1.19582 2.57631 5.55050 .584795 1.72 2•9584 5.08845 1.31149 4.14790 1 19815 2.58133 5.56130 .581395 1.73 2.9929 5.17772 1.31529 4.15933 1.20046 2.58632 5.57205 .578035 1.74 3.0276 5.26802 1.31909 4.17133 1.20277 2.59129 5.58277 .574713 1.75 3.0625 5.35938 1.32288 4.18330 1.20507 2.59625 5.59344 .571429 1.76 3.0976 5.45178 1.32665 4.19524 1.20736 2.60118 5 80401 .568182 1.77 3.1329 5.54523 1. 33041 4.20714 140004 1.00010 5.61467 .564972 1.78 3.1684 5.63975 1.33417 4.21900 1.21192 2.61100 5.62523 .561798 1.79 3.2041 5.73534 1.33791 4.23084 141418 2.61588 5.63574 .558659 1.80 3.2400 5.83200 1.34164 4.24264 1.21644 2.62074 5.64622 .555556 1.81 3.2761 5.92974 1.34536 4.25441 1.21869 2.62558 5.65665 .552486 1.82 3.3124 6.02857 1.34907 4.26615 140000 2.63041 5.66705 .549451 1.83 3.3489 6.12849 1.35277 4.27785 1.22316 2.63522 5.67741 .546448 1.84 3.3586 6.22950 1.35647 4.28952 1.22539 2.64001 5.68773 .543478 1.85 3.4225 6.33163 1.36015 4.30116 1.22760 2.64479 5.69802 .540541 1.86 3.4596 6.43486 1.36382 4.31277 1.22981 2.64954 5.70827 .537634 1.87 3.4969 6.53920 1.36748 4.32435 1.23201 2.65428 5.71848 .534759 1.88 3.5344 6.64467 1.37113 4.33590 1.23420 2.65900 5.72865 .531915 1.89 3.5721 6.75127 1.37477 4.34741 1.23639 2.66371 5.73879 .529101 1.90 3.6100 6.85900 1.37840 446000 1.23856 2.66840 5.74890 .526316 1.91 3.6481 6.96787 1.38203 4.37035 1.24073 2.67307 5.75897 .523560 1.92 3.6864 7.07789 1.38564 4.38178 1.24289 2.67773 5.76900 .520833 1.93 3.7249 7.18906 1.38924 4.39318 1.24505 2.68237 5.77900 .518135 1.94 3.7636 7.30138 1.39284 4.40454 1.24719 2.68700 5.78896 .515464 1.95 3.8025 7.41488 1.39642 4.41588 144000 2.69161 6.70000 .512821 1.96 3.8416 7.52954 1.40000 4.42719 1.25146 2.69620 5.80879 .510204 1.97 8.8800 7.64607 1.40067 4.43847 1.25359 2.70078 5.81865 .507614 1.98 3.9204 7.76239 1.40712 4.44972 1.25571 2.70534 5.82848 .505051 1.99 3.9601 7.88060 1.41067 4.46094 1.25782 2.70989 5.83827 .502513 2.00 4.0000 8.00000 1.41421 4.47214 1.25992 2.71442 5.84804 .500000
 n n2 n3 1/n 2.01 4.0401 8.12060 1.41774 4.48330 1.26202 2.71893 5.85777 .497512 2.02 4.0804 8.24241 1.42127 4.49444 1.26411 2.72343 5.86746 .495050 2.03 4.1209 8.36543 1.42478 4.50555 1.26619 2.72792 5.87713 .492611 2.04 4.1616 8.48966 1.42829 4.51664 1.26827 2.73239 5.88677 .490196 2.05 4.2025 8.61513 1.43178 4.52769 1.27033 2.73685 5.89637 .487805 2.06 4.2436 8.74182 1.43527 4.53872 1.27240 2.74129 5.90594 .485437 2.07 4.2849 8.86974 1.43875 4.54973 1.27445 2.74572 5.91548 .483092 2.08 4.3264 8.99891 1.44222 4.56070 1.27650 2.75014 5.92499 .480769 2.09 4.3681 9.12933 1.44568 4.57165 1.27854 2.75454 5.93447 .478469 2.10 4.4100 9.26100 1.44914 4.58258 1.28058 2.75893 5.94392 .476191 2.11 4.4521 9.39393 1.45258 4.59347 1.28261 2.76330 5.95334 .473934 2.12 4.4944 9.52813 1.45602 4.60435 1.28463 2.76766 5.96273 .471698 2.13 4.5369 9.66360 1.45945 4.61519 1.28665 2.77200 5.97209 .469484 2.14 4.5796 9.80034 1.46287 4.62601 1.28866 2.77633 5.98142 .467290 2.15 4.6225 9.93838 1.46629 4.63681 1.29066 2.78065 5.99073 .465116 2.16 4.6656 10.0777 1.46969 4.64758 1.29266 2.78495 6.00000 .462963 2.17 4.7089 10.2183 1.47309 4.65833 1.29465 2.78924 6.00925 .460830 2.18 4.7524 10.3602 1.47648 4.66905 1.29664 2.79352 6.01846 .458716 2.19 4.7961 10.5035 1.47986 4.67974 1.29862 2.79779 6.02765 .456621 2.20 4.8400 10.6480 1.48324 4.69042 1.30059 2.80204 6.03681 .454546 2.21 4.8841 10.7939 1.48661 4.70106 1.30256 2.80628 6.04594 .452489 2.22 4.9284 10.9410 1.48997 4.71169 1.30452 2.81051 6.05505 .450451 2.23 4.9729 11.0896 1.49332 4.72229 1.30648 2.81472 6.06413 .448431 2.24 5.0176 11.2394 1.49666 4.73286 1.30843 2.81892 6.07318 .446429 2.25 5.0625 11.3906 1.50000 4.74342 1.31037 2.82311 6.08220 .444444 2.26 5.1076 11.5432 1.50333 4.75395 1.31231 2.82728 6.09120 .442478 2.27 5.1529 11.6971 1.50665 4.76445 1.31424 2.83145 6.10017 .440529 2.28 5.1984 11.8524 1.50997 4.77493 1.31617 2.83560 6.10911 .438597 2.29 5.2441 12.0090 1.51327 4.78539 1.31809 2.83974 6.11803 .436681 2.30 5.2900 12.1670 1.51658 4.79583 1.32001 2.84387 6.12693 .434783 2.31 5.3361 12.3264 1.51987 4.80625 1.32192 2.84798 6.13579 .432900 2.32 5.3824 12.4872 1.52315 4.81664 1.32382 2.85209 6.14463 .431035 2.33 5.4289 12.6493 1.52643 4.82701 1.32572 2.85618 6.15345 .429185 2.34 5.4756 12.8129 1.52971 4.83735 1.32761 2.86026 6.16224 .427350 2.35 5.5225 12.9779 1.53297 4.84768 1.32950 2.86433 6.17101 .425532 2.36 5.5696 13.1443 1.53623 4.85798 1.33139 2.86838 6.17975 .423729 2.37 5.6169 13.3121 1.53948 4.86826 1.33326 2.87243 6.18846 .421941 2.38 5.6644 13.4813 1.54272 4.87852 1.33514 2.87646 6.19715 .420168 2.39 5.7121 13.6519 1.54596 4.88876 1.33700 2.88049 6.20582 .418410 2.40 5.7600 13.8240 1.54919 4.89898 1.33887 2.88450 6.21447 .416667 2.41 5.8081 13.9975 1.55242 4.90918 1.34072 2.88850 6.22308 .414938 2.42 5.8564 14.1725 1.55563 4.91935 1.34257 2.89249 6.23168 .413223 2.43 5.9049 14.3489 1.55885 4.92950 1.34442 2.89647 6.24025 .411523 2.44 5.9536 14.5268 1.56205 4.93964 1.34626 2.90044 6.24880 .409836 2.45 6.0025 14.7061 1.56525 4.94975 1.34810 2.90439 6.25732 .408163 2.46 6.0516 14.8869 1.56844 4.95984 1.34993 2.90834 6.26583 .406504 2.47 6.1009 15.0692 1.57162 4.96991 1.35176 2.91227 6.27431 .404858 2.48 6.1504 15.2530 1.57480 4.97996 1.35358 2.91620 6.28276 .403226 2.49 6.2001 15.4382 1.57797 4.98999 1.35540 2.92011 6.29119 .401606 2.50 6.2500 15.6250 1.58114 5.00000 1.35721 2.92402 6.29961 .400000
 n n2 n3 1/n 2.51 6.3001 15.8133 1.58430 5.00999 1.35902 2.92791 6.30799 .398406 2.52 6 8604 16.0030 1.58745 5.01996 1.36082 2.93179 6.31636 .396825 2.53 6.4009 16.1943 1.59060 5.02991 1.36262 2.93567 6.32470 .395257 2 54 6.4516 16.3871 1.59374 5.03984 1.88441 3.80868 6.33303 .393701 2.55 6.5025 16.5814 1.59687 5.04975 148888 2.94338 6.34133 .392157 2.56 6.5536 16.7772 1.60000 5.05964 1.36798 2.94723 6.34960 .390625 2.57 6.6049 16.9746 1.60312 5.06952 1.36976 2.95106 6.35786 .389105 2.58 6.6564 17.1735 1.60624 5.07937 1.37153 2.98488 6.36610 .387597 2.59 6.7081 17.3740 1.60935 5.08920 1.37330 2.95869 6.37431 .386100 2.60 6.7600 17.5760 1.61245 5.09902 1.37507 2.96250 6.38260 .384615 2.61 6.8121 17.7796 1.61555 5.10882 1.37683 2.96629 6.39068 .383142 2.62 6.8644 17.9847 1.61864 5.11859 1.37859 2.97007 6.39883 .381679 2.63 6.9169 18.1914 1.62173 5.12835 1.38034 2.9785 6.40696 .380228 2.64 6.9696 18.3997 1.62481 5.13809 1.38208 2.97761 6.41607 .378788 2.65 7.0225 18.6096 1.62788 5.14783 1.38383 2.98137 848810 .377359 2.66 7.0756 18.8211 1.63095 6.15753 1.38557 2.98511 6.43123 .375940 2.67 7.1289 19.0342 1.63401 5.16720 1.38730 2 80008 6.43928 .374532 2.6- 7.1824 19.2488 1.63707 5.17687 1.38903 2.99257 6.44731 .373134 2.69 T.SS61 19.4651 1.64012 5.18652 1.39076 2.99629 6.45531 .371747 2.70 7.2900 19.6830 1.64317 5.19615 1.39248 3.00000 6.46330 .370370 2.71 7.3441 19.9025 1.64621 5.20577 1.39419 3.00370 6.47127 .369004 2.72 74884 20.1236 1.64924 5.21536 1.39591 3.00739 6.47922 .367647 2.73 7.4529 20.3464 1.65227 5.22494 1.39761 3.01107 6.48715 .366300 2.74 7.5076 20.5708 1.65529 5.23460 1.39932 3.01474 6.49507 .364964 2.75 7.5625 20.7969 1.65831 5.24404 1.40102 3.01841 6.50296 888008 2.76 7.6176 21.0246 1.66132 5.25357 1.40272 3.02206 6.51083 .362319 2.77 7.6729 21.2539 1.66433 5.26308 1.40441 3.02571 6.51868 .361011 2.78 7.7284 21.4850 1.66733 5.27257 1.40610 3.02934 6.52652 .359712 2.79 7.7841 21.7176 1.67033 5.28205 1.40778 3.03297 648484 .358423 2.80 7.8400 21.9520 1.67332 5.29160 1.40946 3.03659 6.54213 .357142 2.81 7.8961 22.1880 1.67631 5.30094 1.41114 3.04020 6.54991 .355872 2.82 7.9524 22.4258 1.67929 5.31037 1.41281 3.04380 6.55767 .354610 2.83 B4088 22.6652 l.68226 5.31977 1.41448 3.04740 6.56541 .353357 2.84 8.0656 22.9063 1.68523 5.32917 1.41614 3.05098 6.57314 .352113 2.86 8.1225 23.1491 1.68819 5.33864 1.41780 3.05456 6.58084 880871 2.86 8.1796 23.3937 1.69115 5.34790 1.41946 3.05813 6.58853 .349650 2.87 8.2369 23.6399 1.69411 5.36724 1.42111 3.06169 6.59620 .348432 2.88 8.2944 23.8879 1.69706 5.36656 1.42276 3 60834 6.60385 .347222 2.89 8.3521 24.1376 1.70000 5.37587 1.42440 3.06878 6.61149 .346021 2.90 8.4100 24.3890 1.70294 5.38516 l.42604 3.07232 6.61911 844808 2.91 8.4681 24.6422 1.70587 5.39444 1.42768 3.07585 6.62671 .343643 2.92 8.5264 24.8971 1.70880 5.40370 1.49801 3.07936 6.63429 .342466 2.93 8.5849 25.1538 1.71172 5.41295 1.43094 8.00987 6.64185 .341297 2.94 8.6438 25.4122 1.71464 6.42218 l.43257 3.08638 644040 .340136 2.95 8.7025 25.6724 1.71756 5.43139 l.43419 3.08987 6.65693 488808 2.96 8.7616 25.9343 1.72047 5.44069 1.43581 3.09336 6.66444 .337838 2.97 8.8209 26.1981 1.72337 5.44977 1 43743 3.09684 6.67194 .336700 2.96 8.8804 26.4636 1.72627 5.45894 1.43904 3.10031 6.67942 .335571 2.99 8.9401 26.7309 1.73205 5.46809 1 14086 3.10878 6.68688 .334448 3.00 9.0000 27.0000 1.73205 5.47723 1.44225 3.10723 6.69433 .333333
 n n2 n3 1/n 3.01 9.0601 27.2709 1.73494 5.48635 1.44385 3.11068 6.70176 .332226 3.02 9.1204 27.5436 1.73781 5.49545 1.44545 3.11412 6.70917 .331126 3.03 9.1809 27.8181 1.74069 5.50454 1.44704 3.11755 6.71657 .330033 3.04 9.2416 28.0945 1.74356 5.51362 1.44863 3.12098 6.72395 .328947 3.05 9.3025 28.3726 1.74642 5.52268 1.45022 3.12440 6.73132 .327869 3.06 9.3636 28.6526 1.74929 5.53173 1.45180 3.12781 6.73866 .326797 3.07 9.4249 28.9344 1.75214 5.54076 1.45338 3.13121 6.74600 .325733 3.08 9.4864 29.2181 1.75499 5.54977 1.45496 3.13461 6.75331 .324675 3.09 9.5481 29.5036 1.75784 5.55878 1.45653 3.13800 6.76061 .323625 3.10 9.6100 29.7910 1.76068 5.56776 1.45810 3.14138 6.76790 .322581 3.11 9.6721 30.0802 1.76352 5.57674 1.45967 3.14475 6.77517 .321543 3.12 9.7344 30.3713 1.76635 5.58570 1.46123 3.14812 6.78242 .320513 3.13 9.7969 30.6643 1.76918 5.59464 1.46279 3.15148 6.78966 .319489 3.14 9.8596 30.9591 1.77200 5.60357 1.46434 3.15484 6.79688 .318471 3.15 9.9225 31.2559 1.77482 5.61249 1.46590 3.15818 6.80409 .317460 3.16 9,9856 31.5545 1.77764 5.62139 1.46745 3.16152 6.81128 .316456 3.17 10.0489 31.8550 1.78045 5.63028 1.46899 3.16485 6.81846 .315457 3.18 10.1124 32.1574 1.78326 5.63915 1.47054 3.16817 6.82562 .314465 3.19 10.1761 32.4618 1.78606 5.64801 1.47208 3.17149 6.83277 .313480 3.20 10.2400 32.7680 1.78885 5.65685 1.47361 3.17480 6.83990 .312500 3.21 10.3041 33.0762 1.79165 5.66569 1.47515 3.17811 6.84702 .311527 3.22 10.3684 33.3862 1.79444 5.67450 1.47668 3.18140 6.85412 .310559 3.23 10.4329 33.6983 1.79722 5.68331 1.47820 3.18469 6.86121 .309598 3.24 10.4976 34.0122 1.80000 5.69210 1.47973 3.18798 6.86829 .308642 3.25 10.5625 34.3281 1.80278 5.70088 1.48125 3.19125 6.87534 .307692 3.26 10.6276 34.6460 1.80555 5.70964 1.48277 3.19452 6.88239 .306749 3.27 10.6929 34.9658 1.80831 5.71839 1.48428 3.19779 6.88942 .305810 3.28 10.7584 35.2876 1.81108 5.72713 1.48879 3.20104 6.89643 .304878 3.29 10.8241 35.6129 1.81384 5.73585 1.48730 3.20429 6.90344 .303951 3.30 10.8900 35.9370 1.81659 5.74456 1.48881 3.20753 6.91042 .303030 3.31 10.9561 36.2647 1.81934 5.75326 1.49031 3.21077 6.91740 .302115 3.32 11.0224 36.5944 1.82209 5.76194 1.49181 3.21400 6.92436 .301205 3.33 11.0889 36.9260 1.82483 5.77062 1.49330 3.21723 6.93130 .300300 3.34 11.1556 37.2597 1.82757 5.77927 1.49480 3.22044 6.93823 .299401 3.35 11.2225 37.5954 1.83030 5.78792 1.49629 3.22365 6.94515 .298508 3.36 11.2896 37.9331 1.83303 5.79655 1.49777 3.22686 6.95205 .297619 3.37 11.3569 38.2728 1.83576 5.80517 1.49926 3.23005 6.95894 .296736 3.38 11.4244 38.6145 1.83848 5.81378 1.50074 3.23325 6.96582 .295858 3.39 11.4921 38.9582 1.84120 5.82237 1.50222 3.23643 6.97268 .294985 3.40 11.5600 39.3040 1.84391 5.83095 1.50369 3.23961 6.97953 .294118 3.41 11.6281 39.6518 1.84662 5.83952 1.50517 3.24278 6.98637 .293255 3.42 11.6964 40.0017 1.84932 5.84808 1.50664 3.24595 6.99319 .292398 3.43 11.7649 40.3536 1.85203 5.85662 1.50810 3.24911 7.00000 .291545 3 44 11.8336 40.7076 1.85472 5.86515 1.50957 3.25227 7.00680 .290698 3.45 11.9025 41.0636 1.85742 5.87367 1.51103 3.25542 7.01358 .289855 3.46 11.9716 41.4217 1.86011 5.88218 1.51249 3.25856 7.02035 .289017 3.47 12.0409 41.7819 1.86279 5.89067 1.51394 3.26169 7.02711 .288184 3.48 12.1104 42.1442 1.86548 5.89915 1.51540 3.26482 7.03385 .287356 3.49 12.1801 42.5085 1.86815 5.90762 1.51685 3.26795 7.04058 .286533 3.50 12.2500 42.8750 1.87083 5.91608 1.51829 3.27107 7.04730 .285714
 n n2 n3 1/n 3.51 12.3201 43.2436 1.87350 5.92453 1.51974 3.27418 7.05400 .284900 3.52 12.3904 43.6142 1.87617 5.93296 1.52118 3.27729 7.06070 .284091 3.53 12.4609 43.9870 1.87883 6.84188 1.52262 3.28039 7.06738 .283286 3.54 12.5316 44.3619 1.88149 5.94979 1.52406 3.28348 7.07404 .282486 3.55 12.6025 44.7389 1.88414 5.95816 1.52549 3.28657 7.08070 .281690 3.56 12.6736 45.1180 1.88680 5.96657 1.52692 3.28965 7.08734 .280899 3.57 12.7449 46.4993 1.88944 5.97495 1.52835 3.29273 7.09397 .280112 3.58 12.8164 664037 1.89209 5.98331 1.52978 3.29580 7.10059 .279330 3.59 12.8881 46.2683 1.89473 5.99166 1.53120 3.29887 7.10719 .278552 3.60 12.9600 46.6560 1.89737 6.00000 1.53262 3.30193 7.11379 .277778 3.61 13.0321 47.0459 1.90000 6.00833 1.53404 3.30498 7.12037 .277008 3.62 13.1044 47.4379 1.90263 6.01664 1.53545 3.30803 7.12694 .276243 3.63 13.1769 47.8321 1.90526 6.02495 1.53686 3.31107 7.13349 .275482 364 13.2496 48.2285 1.90788 6.03324 1.53827 3.31411 7.14004 .274725 3.65 13.3225 48.6271 1.91050 6.04152 1.53968 3.31714 7.14657 .273973 3.66 13.3956 49.0279 1.91311 6.04979 1.54109 3.32017 7.15309 .273224 3.67 13.4689 49.4309 1.91572 6.05805 1.54249 3.32319 7.15960 .272480 3.68 13.5424 49.8360 1.91833 6.06630 1.54389 3.32621 7.16610 .271739 3.69 13.6161 50.2434 1.92094 6.07454 1.54529 3.32922 7.17258 .271003 3.70 13.6900 50.6530 1.92354 6.08276 1.54668 3.33222 7.17905 .270270 3.71 13.7641 51.0648 1.92614 6.09098 1.54807 3.33522 7.18552 .269542 \$.72 18.8384 51.4788 6.09918 1.54946 3.33822 7.19197 .268817 3.73 104130 614061 1.93132 6.10737 155085 3.34120 7.19841 .268097 8.74 13.9876 52.3136 1.99391 6.11555 1.55223 3.34419 7.20483 .267380 8.75 14.0625 52.7344 1.93649 6.12372 1.55362 3.34716 7.21125 .266667 3.76 14.1376 53.1574 1.93907 6.13188 1.55500 3.35014 7.21765 .265957 3.77 14.2129 53.5826 1.94165 6.14003 1.55637 3.35310 7.22405 .265252 3.78 14.2884 54.0102 1.94422 6.14817 1.55775 3.35607 7.23043 .264550 3.79 14.3641 64.4880 1.94679 6.15630 1.55912 3.35902 7.23680 .263852 3.80 14.4400 54.8720 1.94936 6.16441 1.56049 3.36188 7.24316 .263158 3.81 14.5161 55.3063 1.95192 6.17252 1.56186 3.36492 7.24950 .262467 3.82 14.5924 55.7430 1.95448 6.18061 1.56322 3.36786 7.25584 .261780 3.83 1 4 8888 56.1819 1.95704 6.18870 1.56459 3.37080 7.26217 .261097 3.84 56.6231 l.95959 6.19677 1.56595 3.37373 7.26848 .260417 3.85 14.8225 57.06666 1.96214 6.20484 1.56731 3.37666 7.27479 .259740 3.86 14.8996 57.5125 1.96469 6.21289 1.56866 3.37958 7.28108 .259067 3.87 14.9769 57.9606 1.96723 6.22093 1..57001 3.38249 7.28736 .258398 3.88 15.0544 58.4111 l.96977 6.22896 1.57137 3.38540 7.29363 ..2577322. 3.89 15.1321 58.8639 1.97231 6.23699 1.57271 3.38831 7.29989 .257069 3 90 15.2100 59.3190 1.97484 6.24500 1.57406 3.39121 7.30614 .256410 3.91 15.2881 59.7765 1.97737 6.25300 1.57541 3.39411 7.31238 .255755 3.92 15.3664 60.2363 l.97990 6.26099 l .57675 3.39700 7.31861 .255102 3.93 15.4449 60.6985 1.98242 6.26897 1.57809 3.39988 7.32483 .254453 3.94 15.5236 61.1630 1.98494 6.27694 1.57942 3.40277 7.33104 .253807 3.95 15.6025 61.6299 1.98746 6.28490 1.58076 3.40564 7.33723 .253165 3.96 15.6816 014001 1.98997 6.29285 1.58209 3.40851 7.34342 .252525 3.97 15.7609 62.5708 1.99249 6.30079 1.58342 3.41138 7.34960 .251889 3.98 164404 63.0448 1.99499 6.30872 1.58475 3.41424 7.35576 .251256 3.99 15.9201 63.5212 1.99750 6.31664 1.58608 3.41710 7.36192 .250627 4.00 16.0000 64.0000 2.00000 6.32456 1.58740 3.41995 7.36806 .250000
 n n2 n3 1/n 4.01 16.0801 64.4812 2.00250 6.33246 1.58872 3.42280 7.37420 .249377 4.02 16.1604 64.9648 2.00499 6.34035 1.59004 3.42564 7.38032 .248756 4.03 16.2409 65.4508 2.00749 6.34823 1.59136 3.42848 7.38644 .248139 4.04 16.3216 65.9393 2.00998 6.35610 1.59267 3.43131 7.39254 .247525 4.05 16.4025 66.4301 2.01246 6.36396 1.59399 3.43414 7.39864 .246914 4.06 16.4836 66.9234 2.01494 6.37181 1.59530 3.43697 7.40472 .246305 4.07 16.5649 67.4191 2.01742 6.37966 1.59661 3.43979 7.41080 .245700 4.08 16.6464 67.9173 2.01990 6.38749 1.59791 3.44260 7.41686 .245098 4.09 16.7281 68.4179 2.02237 6.39531 1.59922 3.44541 7.42291 .244499 4.10 16.8100 68.9210 2.02485 6.40312 1.60052 3.44822 7.42896 .243902 4.11 16.8921 69.4265 2.02731 6.41093 1.60182 3.45102 7.43499 .243309 4.12 16.9744 69.9345 2.02978 6.41872 1.60312 3.45382 7.44102 .242718 4.13 17.0569 70.4450 2.03224 6.42651 1.60441 3.45661 7.44703 .242131 4.14 17.1396 70.9579 2.03470 6.43428 1.60571 3.45939 7.45304 .241546 4.15 17.2225 71.4734 2.03715 6.44205 1.60700 3.46218 7.45904 .240964 4.16 17.3056 71.9913 2.03961 6.44981 1.60829 3.46496 7.46502 .240385 4.17 17.3889 72.5117 2.04206 6.45755 1.60958 3.46773 7.47100 .239808 4.18 17.4724 73.0346 2.04450 6.46529 1.61086 3.47050 7.47697 .239234 4.19 17.5561 73.5601 2.04695 6.47302 1.61215 3.47327 7.48292 .238664 4.20 17.6400 74.880 2.04939 6.48074 1.61343 3.47603 7.48887 .238095 4.21 17.7241 74.6185 2.05183 6.48845 1.61471 3.47878 7.49481 .237530 4.22 17.8084 75.1514 2.05426 6.49615 1.61599 3.48154 7.50074 .236967 4.23 17.8929 75.6870 2.05670 6.50385 1.61726 3.48428 7.50666 .236407 4.24 17.9776 76.2250 2.05913 6.51153 1.61853 3.48703 7.51257 .235849 4.25 18.0625 76.7656 2.06155 6.51920 1.61981 3.48977 7.51847 .235294 4.26 18.1476 77.3088 2.06398 6.52687 1.62108 3.49250 7.52437 .234742 4.27 18.2329 77.8545 2.06640 6.53452 1.62234 3.49523 7.53025 .234192 4.28 18.3184 78.4028 2,06882 6.54217 1.62361 3.49796 7.53612 .233645 4.29 18.4041 78.9536 2.07123 6.54981 1.62487 3.50068 7.54199 .233100 4.30 18.4900 79.5070 2.07364 6.55744 1.62613 3.50340 7.54784 .232558 4.31 18.5761 80.0630 2.07605 6.56506 1.62739 3.50611 7.55369 .232019 4.32 18.6624 80.6216 2.07846 6.57267 1.62865 3.50882 7.55953 .231482 4.33 18.7489 81.1827 2.08087 6.58027 1.62991 3.51153 7.56535 .230947 4.34 18.8356 81.7465 2.08327 6.58787 1.63116 3.51423 7.57117 .230415 4.35 18.9225 82.3129 2.08567 6.59545 1.63241 3.51692 7.57698 .229885 4.36 19.0096 82.8819 2.08806 6.60303 1.63366 3.51962 7.58279 .229358 4.37 19.0969 83.4535 2.09045 6.61060 1.63491 3.52231 7.58858 .228833 4.38 19.1844 84.0277 2.09284 6.61816 1.63616 3.52499 7.59436 .228311 4.39 19.2721 84.6045 2.09523 6.62571 1.63740 3.52767 7.60014 .227790 4.40 19.3600 85.1840 2.09762 6.63325 1.63864 3.53035 7.60590 .227273 4.41 19.4481 85.7661 2.10000 6.64078 1.63988 3.53302 7.61166 .226757 4.42 19.5364 86.3509 2.10238 6.64831 1.64112 3.53569 7.61741 .226244 4.43 19.6249 86.9383 2.10476 6.65582 1.64236 3.53835 7.62315 .225734 4.44 19.7136 87.5284 2.10713 6.66333 1.64359 3.54101 7.62888 .225225 4.45 19.8025 88.1211 2.10950 6.67083 1.64483 3.54367 7.63461 .224719 4.46 19.8916 88.7165 2.11187 6.67832 1.64606 3.54632 7.64032 .224215 4.47 19.9809 89.3146 2.11424 6.68581 1.64729 3.54897 7.64603 .223714 4.48 20.0704 89.9154 2.11660 6.69328 1.64851 3.55162 7.65172 .223214 4.49 20.1601 90.5188 2.11896 6.70075 1.64974 3.554X6 7.65741 .222717 4.50 20.2500 91.1250 2.12132 6.70820 1.65096 3.55689 7.66309 .222222