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Ηλεκτρ. έκδοση

=

first and second significant figures, the number 1.29684 is found between 1.29664 = 2.18 and 1.29862 = 2.19. The first difference is 198; the second difference is 20; and 20 ÷ 198 = .101+, or .10. Hence, the first five significant figures are 21810; the number of figures in the integral part of the cube is 3 X 3 - 27; and 129.6843 = 2,181,000, correct to five significant figures.

(b) 7.64420 occurs between 7.64032 446 and 7.64603 = 447. The first difference is 571; the second difference is 388; and 388 ÷ 571.679+, or .68. Hence, the first five significant figures are 44668; the number of ciphers following the decimal point is 3 X 0 = 0; and .764423= .44668, correct to five significant figures.

(c) 3.2425 falls between 3.24278 =

34.1 and 3.23961

34.0. The first difference is 317; the second difference is 289; 289 317.911+, or .91. Hence, the first five significant figures are 34091; the number of ciphers following the decimal point is 3X1 + 1 = 4; and .0324253= .000034091, correct to five significant figures.

RECIPROCALS.

a

The reciprocal of a number is 1 divided by the number. By using reciprocals, division is changed into multiplication, since a b = 1 = a × 1 The table gives the reciprocals of b 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 recip rocal 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 determine the fourth and fifth figures.

n

EXAMPLE.

(a) The reciprocal of 379.426 =? (b) ·

[merged small][ocr errors]

2194 = .129+, or .13. Hence, five significant figures.

1

.0004692
1
2.64

=

1440;

1 .380228 The first difference is 380228 - 378788 2.63* the second difference is 380228

379426 802; 802 1440 .557, or .56. Hence, the first five significant figures are 26356, and the reciprocal of 379.426 is .0026356, to five significant figures.

1

1 (b) .469200 falls between .469484 and .467290 2.13 2.14 The first difference is 2194; the second difference is 284; 284

1 .0004692

2131.3, correct to

?

=

and

[merged small][ocr errors]

1.06

1.1236

1.07

1 1449 1.08 1.1664 1.09 1.1881 1.10 1.2100

1.11

1.12

1.13

1.01

1.0201 1.03030 1.00499 3.17805 1.00332 1.02 1.0404 1.06121 1.00995 3.19374 1.03 1.0609 1.09273 1.01489 3.20936 1.04 1.0816 1.12486 1.01980 3.22490 1.05 1.1025 1.15763 1.02470 3.24037

[ocr errors]

1.34 1.35

1.19102 1.02956 3.25576
1.22504 1.03441 3.27109
1.25971 1.03923 3.28634
1.29503 1.04403 3.30151
1.33100 1.04881 3.31662

1

n

.990099 .980392

2.16159 4.65701 1.00662 2.16870 4.67233 1.00990 2.17577 4.68755 1.01316 2.18278 4.70267 .961539 1.01640 2.18976 4.71769 .952381

.970874

1.2321
1.2544

1 36763 1.05357 3.33167 1.03540 2.23070 1.40493 1.05830 3.34664 1.03850 2.23738 1.2769 1.44290 1.06301 3.36155 1.04158 2.24402 1.14 1.2996 1.48154 1.06771 3.37639 1.04464 2.25062 1.15 1.3225 1.52088 1.07238 3.39116 1.04769 2.25718 1.16 1.3456 1.17 1.3689 1.18 1.3924 1.19 1.4161 1.20 1.4400 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

1.01961 2.19669 4.73262 .943396 1.02281 2.20358 4.74746 .934579 1.02599 2.21042 4.76220 .925926 1.02914 2.21722 4.77686 .917431 1.03228 2.22398 4.79142 .909091

1.08008 1.08 1.08577 1.08859 1.30 1.6900 2.19700 1.14018 3.60555 1.09139

1.26 1.5876 2.00038 1.12250 3.54965
1.27 1.6129 2.0.
1.12694 3.56371
1.28 1.6384 2.09715 1.13137 3.57771
1.29 1.6641 2.14669 1.13578 3.59166

4.80590 .900901 4.82028

.892857

4.83459

.884956

4.84881 .877193 4.86294 .869565

1.56090 1.07703 3.40588 1.05072 2.26370 4.87700 .862069 1.60161 1.08167 3.42053 1.05373 2.27019 4.89097 .854701 1.64303 1.08628 3.43511 1.05672 2.27664 4.90487 .847458 1.68516 1.09087 3.44964 1.05970 2.28305 4.91868 .840336 1.72800 1.09545 3.46410 1.06266 2.28943 4.93242 .833333

2.32697 5.01330 .793651 2.33310 5.02653 .787402 2.33921 5.03968 .781250 2.34529 5.05277 .775194 2.35134 5.06580 .769231

.763359 .757576

1.31 1.7161 2.24809 1.14455 3.61939 1.09418 2.35735 5.07875 1.32 1.7424 2.29997 1.14891 3.63318 1.09696 2.36333 5.09164 1.33 1.7689 2.35264 1.15326 3.64692 1.09972 2.36928 5.10447 .751880 1.7956 2.40610 1.15758 3.66060 1.10247 1.8225 2.46038 1.16190 3.67423 1.10521

2.37521 5.11723 .746269 2.38110 5.12993 .740741

1.10793 2.38696 5.14256 .735294

1.36
1.37
1.38 1.9044 2.62807 1.17473 3.71484 1.11334 2.39861

1.8496 2.51546 1.16619 3.68782
1.8769 2.57135 1.17047 3.70135 1.11064 2.39280

5.15514 .729927

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 5.21710 .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 1.48 2.1904 3.24179 1.21655 3.84708 1.13960 2.45520 5.28957 1.49 2.2201 3.30795 1.22066 3.86005 1.14216 2.46072 5.30146 1.50 2.2500 3.37500 1.22474 3.87298 1.14471 2.46621 5.31329 .666667

.680272

.675676 .671141

2

√n

in

1.51 2.2801 3.44295 1.22882 3.88587 1.14725
1.52 2.3104 3.51181 1.23288 3.89872
1.53
2.3409 3.58158 1.23693 3.91152
1.54 2.3716 3.65226 1.24097 3.92428
1.55 2.4025 3.72388 1.24499 3.93700

V10 n V100 n

.662252 .657895 .653595

2.47168 5.32507 1.14978 2.47713 5.33680 1.15230 2.48255 5.34848 1.15480 2.48794 5.36011 .649351 1.15729 2.49332 5.37169.645161 2.49866 5.38321 .641026 2.50399 5.39469 .636943 2.50930 5.40612 .632911

1.56 2.4336 3.79642 1.24900 3.94968 1.15978 1.57 2.4649 3.86989 1.25300 3.96232 1.16225 1.58 2.4964 3.94431 1.25698 3.97492 1.16471 1.59 2.5281 4.01968 1.26095 3.98748 1.16717 2.51458 5.41750 .628931 2.5600 4.09600 1.26491 4.00000 1.16961 2.51984 5.42884 .625000

1.60

[ocr errors]

n2

1.66 2.7556 1.67 2.7889 1.68 2.8224 1.69 2.8561 1.70 2.8900 1.71 2.9241 1.72 2.9584 1.73 2.9929 1.74 3.0276

1.75 3.0625

n3

V10 n

1.81 3.2761 1.82 3.3124 3.3489 1.84 3.3-56 1.85 3.4225

1.83

1.61 2.5921 4.17328 1.26886 4.01248 1.17204 2.52508 5.44012 .621118 1.62 2.6244 4.25153 1.27279 4.02492 1.17446 2.53030 5.45136 .617284 1.63 2.6569 4.33075 1.27671 4.03733 1.17687 2.53549 5.46256 .613497 2.6896 4.41094 1.28062 4.04969 1.17927 2.54067 5.47370 .609756 2.7225 4.49213 1.28452 4.06202 1.18167 2.54582 5.48481 .606061

1.64

1.65

4.57430 1.28841 4.07431 1.18405 2.55095
4.65746 1.29228 4.08656 1.18642 2.55607

4.74163 1.29615 4.09878 1.18878 2.56116 5.51785 .595238
4.82681 1.30600 4.11096 1.19114 2.56623 5.52877
4.91300 1.30384 4.12311 1.19348 2.57128 5.53966

.591716
.588235

1.76 3.0976 5.45178 1.32665 4.19524 1.20736 2.60118 | 5.60408
1.77 3.1329 5.54523 1.33041 4.20714 1.20964 2.60610 5.61467
1.78 3.1684 5.63975 1.33417 4.21900
1.79
3.2041 5.73534 1.33791 4.23084
1.80 3.2400 5.83200 1.34164 4.24264 1.21644 2.62074 5.64622

1.21192 2.61100 5.62523
1.21418 2.61588 5.63574

1

5.92974 1.34536 4.25441
6.02857 1.34907 4.26615
6.1:849 1.35277 4.27785
6.22950 1.35647 4.28952
6.33163 1.36015 4.30116

5.00021 1.30767 4.13521 1.19582 2.57631 5.55050 .584795 5.08845 1.31149 4.14729 1.19815 2.58133 5.56130 .581395 5.17772 1.31529 4.15933 1.20046 2.58632 5.57205 .578035 5.26 02 1.31909 4.17133 1.20277 2.59129 5.58277 .574713 5.35938 1.32288 4.18330 1.20507 2.59625 5.59344 .571429

n

5.49586.602410 5.50688.598802

1.21869 2.62558 5.65665
1.22093 2.63041 5.66705
1.22316 2.63522 5.67741
1.22539 2.64001 5.68773
1.22760 2.64479 5.69802

1.86 3.4596 6.43486 1.36382 4.31277 1.22981
1.87
3.4969 6.53920 1.36748 4.32435 1.23201
1.88 3.5344 6.64467 1.37113 4.33590
1.89 3.5721 6.75127 1.37477 4.34741
1.90 3.6100 6.85900 1.37840 4.35890

.568182

.564972 .561798 .558659

.555556

1.25146 2.69620 5.80879
1.25359 2.70078 5.81865
1.25571 2.70534 5.82848
1.25782 2.70989 5.83827
1.25992 2.71442

5.84804

.552486 .549451

.546448

.543478

.540541

.537634 .534759

2.64954 5.70827 2.65428 5.71848 1.23420 2.65900 5.72865 1.23639 2.66371 5.73879

.531915

.529101

1.23856 2.66840 5.74890 .526316

.515464 .512821

1.91 3.6481 6.96787 1.38203 4.37035 1.24073 2.67307 1.92 3.6864 7.07789 1.38564 4.38178 1.24289 2.67773 5.76900 .520-33 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 1.95 3.8025 7.41488 1.39642 4.41588 1.24933 2.69161 5.79889 1.96 3.8416 7.52954 1.40000 4.42719 1.97 3.8809 7.64537 1.40357 4.43847 1.98 3.9204 7.76239 1.40712 4.44972 1.99 3.9601 7.88060 1.41067 4.46094 2.00 4.0000 8.00000 1.41421 4.47214

5.75897.523560

.510204

.507614

.505051

.502513

.500000

2

√n

√10 nvn

2.73685 5.89637.487805

8.12060 1.41774 4.48330 8.24241 1.42127 4.49444 8.36543 1.42478 4.50555 8.48966 1.42829 4.51664 8.61513 1.43178 4.52769 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 2.08 4.3264 8.99891 1.44222 4.56070 1.27650 2.75014 5.92499 2.09 4.3681 9.12933 1.44568 4.57165 1.27854 2.75454 5.93447 2.10 4.4100 9.26100 1.44914 4.58258 1.28058 2.75893 5.94392

2.06

.483092

.480769

.478469

.476191

2.11

2.12

2.01 4.0401 2.02 4.0804 2.03 4.1209 2.04 4.1616 2.05 4.2025

2.13

2.14 2.15

[ocr errors]

n3

1.26202

1.26411

1.26619

1.26827
1.27033

10n 100 n

2.71893
2.72343 5.86746.495050
2.72792 5.87713.492611

4.4521

9.39393 1.45258 4.59347 1.28261 2.76330 5.95334
4.4944
9.52813 1.45602 4.60435 1.28463 2.76766 5.96273
4.5369 9.66360 1.45945 4.61519 1.28665 2.77200 5.97209
4.5796
9.80034 1.46287 4.62601
4.6225 9.93838 1.46629 4.63681

1.28866 2.77633 5.98142
1.29066 2.78065 5.99073

2.732395.88677 .490196

1

n

5.85777 .497512

2.26

5.1076 2.27 1529 2.28 5.1984

11.5432 1.50333 4.75395 1.31231
11.6971 1.50665 4.76445 1.31424
11.8524 1.50997 4.77493 1.31617

2.29 5.2441 12.0090 1.51327 4.78539 1.31809

2.30 5.2900 12.1670 1.51658
2.31 5.3361 12.3264 1.51987 4.80625 1.32192 2.84798 6.13579
2.32 5.3824 12.4872 1.52315 4.81664 1.32382 2.85209 6.14463
2.33 5.4289 12.6493 1.52643 4.82701
2.34
5.4756 12.8129 1.52971 4.83735
2.35 5.5225

2.46 6.0516 14.8869 1.56844 4.95984 2.47 6.1009 15.0692 1.57162 4.96991 2.48 6.1504 15.2530 1.57480 4.97996 2.49 6.2001 15.4382 1.57797 4.98999 2.50 6.2500 15.6250 1.58114 5.00000

1.29266 2.78495 6.00000
1.29465 2.78924 6.00925

.462963
.460830

.454546

2.16 4.6656 10.0777 1.46969 4.64758 2.17 4.7089 10.2183 1.47309 4.65833 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 2.21 4.8841 2.22 4.9284 2.23 4.9729 2.24 5.0176 2.25

5.0625

10.7939 1.48661 4.70106 1.30256 2.80628 6.04594 .452489
10.9410 1.48997 4.71169 1.30452 2.81051 6.05505 .450451
11.0896 1.49332 4.72229 1.30648 2.81472 6.06413
11.2394 1.49666 4.73286 1.30843 2.81892 6.07318
11.3906 1.50000 4.74342 1.31037 2.82311 6.08220

.448431
.446429

.444444

2.82728 6.09120 .442478 2.83145 6.10017 .440529 2.83560 6.10911 .438597

2.83974 6.11803 .436681 4.79583 1.32001 2.84387 6.12693 .434783

2.36 5.5696 13.1443 1.53623 4.85798
2.37 5.6169 13.3121 1.53948 4.86826
2.38 5.6644 13.4813 1.54272 4.87852
2.39 5.7121 13.6519 1.54596 4.88876
2.40 5.7600 13.8240 1.54919 4.89898
2.41 5.8081 13.9975 1.55242 4.90918
2.42 5.8564 14.1725 1.55563 4.91935
2.43 5.9049 14.3489 1.55885 4.92950 1.34442 2.89647 6.24025
2.44 5.9536 14.5268
2.45 6.0025 14.7061

1.34072
1.34257

2.88850 6.22308
2.89249 6.23168

1.56205 4.93964 1.34626 2.90044
1.5652 4.94975 1.34810 2.90439

.473934

.471698

.469484 .467290

.465116

.432900 .431035

1.32572 2.85618 6.15345 .429185 1.32761 12.9779 1.53297 4.84768 1.32950

2.86026 6.16224 .427356 2.86433 6.17101 .425532

1.335142.87646

1.33700 2.88049

1.33887

1.33139

2.86838 6.17975 .423729 1.33326 2.87243 6.18846 .421941

6.19715 .420168 6.20582 .418410 2.88450 6.21447 .416667

.414938

.413223

.411523

6.24880 .409836

6.25732.408163

.404858

1.34993 2.90834 6.26583 .406504
1.35176 2.91227 6.27431
1.35358 2.91620 6.28276
1,35540 2.92011 6.29119
1.35721 2.92402 6.29961

.403226

.401606 .400000

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