.28 IhCC' Lc^h HPsegg-LM"""""'"''""-"""^ ^Miri'mmmJ,^,?!?."'"^'^"* °' numbers from 3 1924 013 879 212 Beta gorfe £>tate College of Agriculture at Cornell ©niticrsttp atljaca. M. §. 2.ilirarp •— TABLE LIBRARY AUG 8 i^3g agric. econ <^ Farm mgt. OF THE Equivalents of Numbers FROM 1 to 10,000 BY I. P. LAUGHLIN PRINTED BY HENRY CONOLLY CO. 46 STONE STREET. ROCHESTER. N. Y. CopyriBhted 1912 by IP. Laugfhlin. All rights re«erved. . *» Published by IP. LauBhlin, 53 Prentis St , Detroit, Mich. PRICE $5.00 >- if»— HOME PHONE 396S jai^^lii^^i^iiHMie 302 CENTRAL BL'D'G BELL 376 MAIN '^Wi^T W ROCHESTER, N. Y. THIS IS TO CERTIFY We have examined every equivalent contained in the following "Table of Equivalents of Numbers" and in every case they are correct to at least seven decimals. Used for the purpose of determining percentages, five figures up to 10000, these equivalents will give correct results for at least 4 decimal places. We have made thorough tests of the cases to which they may be put, and we unhesitatingly recommend their use for determining ratios or where division by large numbers is required. Used with an adding machine adapted for multiplication of figures the time consumed in obtaining correct results is only a very small fraction of the time required to work the problems by the regular method. W. SALVIN TAYLOR & CO. /f-^ ^;^.. EXPLANATIONS AND ILLUSTRATIONS These Tables of Equivalents or Reciprocals are compiled to facilitate the work of detennining ratio or percentages, or any other work where division is required. By the use of an adding machine such work can be accomplished in a very small fraction of the time which would be consumed by the ordinary method of division. The equivalent of any number required is readily found by reference to the "hundreds" (the Major Key) at the head of each column, with the margin Kej' printed on each side of every Page. Example : — To find the equivalent of 4357. Turn to "4000 to 4500. ' ' The fourth column of the right hand page is keyed 4300 ds and in that column opposite the margin key 57, the reciprocal is found to be .0002295157. (This equivalent multiplied by 4357 will produce .9999999+, being within less than 1 millionth of the complete number 1. (100 percent.) The same will apply to every equivalent found in the tables, aU being correct to the 7th decimal at least. In illustration No. 1 $4357.00 is used as the price of a contract, and the ratio to that amount of the various items of expense and balance of profit are arrived at by the use of the equivalent. Anitemof "printing" is $214.00. To determine the ratio this amount bears to the total, 1214.00 has to be divided by 4357. Instead of using that cumbersome method, it is only necessary to multipty the equivalent by 214, pointing off the decimals used, and the ratio 214 bears to 4357 is the product. The equivalent multiplied by its number producing 1 (or 100%) it follows that multiplied by any other number it will produce the ratio such number bears to the reciprocal nimiber. The uses to which these equvialents can be put are without limit, and will apply to every class of business. A few illustrations are appended, and others for application to any class of business, percentage, measurements, weights, etc. will be gladly furnished on application. ILLUSTRATION No. 1 The total amount received on a contract was $4357.00. An analysis of the cost of completing the contract discloses the following expenditures, and by using the equivalent of 4357 and multipl5dng same by the amounts of the respective items the % cost of each item together with the % of profit is ascertained correctly and quickly (less than 2 minutes). Cost % Material $1243.00 28.5288 Labor 1432.00 32.8666 Advertising 312.00 7.1609 Printing 214.00 4.9116 Legal 65.00 1.4919 Traveling 43.00 9869 Cartage, etc 64.00 1.4689 Express 17.00 3902 Miscellaneous 14.00 3213 Total cost 3404.00 78.1271 Profit 953.00 21.8728 Total amount $4357.00 99.9999 We find the equivalent for "4357," (the total cost of the contract), to be .0002295157. Multiply this equivalent by $1243. (the amoimt of the cost of material) and the result is .S^B@6. yiSZlh To find the percentages of the other items multiply the equivalent of the total cost by the amount of the cost-of each item. All per cents, of this illustration were figured in one minute and forty-five seconds. ILLUSTRATION No. 2 Bought 12,142 articles at $1.32 per gross. How many gross were purchased and what was the total cost ? Ans. —84.3194 +gross. —Total cost $1 1 1 .30. Time for figuring this illustration 17 seconds. Here we find the equivalent for the number in one gross (144) to be .006944444) Multiply this equivalent by 12,142 (the number of pieces purchased) and we have 84.3194 + gross. Multiply the number of gross by $1.32 (the price per gross, and we have $111.30, the total cost. ILLUSTRATION No. 3 Bought 3122 articles at 11^ cents per dozen. How many dozen were purchased and what was total cost? Ans. 260.166+dozen. Total cost $29.27. Time 15 seconds. We find the equivalent for the number in one dozen (12) to be .08333333. Multiply this equivalent by 3122 (the number of pieces bought) and we have 260.166+dozen. Multiply the number of dozen by 11^ cents (the price per one dozen) and we have $29.27 the total cost. ILLUSTRATION No. 4 A man working 23 days makes 1510 articles. What is the average number of articles per day. We find the equivalent for 23 to be .04347826. Multiply this equivalent by 1510, pointing off eight places, that being the number of decimal places in the equivalent. This gives the average number per day of 65.65. Time for figuring this illustration nine seconds. ILLUSTRATION No. 5 672 yards of silk cost $954.24. What is the cost per yard ? We find the equivalent for 672 to be .001488095. Multiply this equivalent by 954.24, pointing off eleven places, (having nine decimal places in our equivalent and two decimal places in 954.24). This gives $1.42 per yard. Time for figuring this illustration 15 seconds. ILLUSTRATION No. 6 An article cost $25.00 and sold for $38.00. What is the per cent, of profit on selling price? Ans. — 34211%. Time for figuring this illustration 11 seconds. Here we find the equivalent for 38 to be .026315789. Multiply this equivalent by $25 and we have 657894725. Having nine decimal places in the equivalent we point off nine places giving us .65789 + . These figures subtracted from 1 .00000 (this representing 100%) gives us a remainder of .34211 which is the per cent, of profit on the selling price. ILLUSTRATION No. 7 An article cost $14.75. What is the selHng price to make 25% profit on selHng price? Answer $19.67. Time]12 seconds. 100% less 25% = 75%. Multiply the equivalent for 75, which is .01333333 by $14.75 and we get 1966666175; having eight decimal places in our equivalent and two decimal places in $14.75, we point off ten places and we have .196666+ or 1% of the selling price; this mtiltiplied by 100, gives us $19.67, or the selling price. ILLUSTRATION No. 8 NET SALES Material used Freight Manufacturing Expense: — Depreciation : — Machinery and Plant Real Estate and Buildings . Patterns Fuel Insurance Light. 167209.36 100.00 791.42 383.15 2429.82 708.49 1749.95 269.23 Labor 44942.00 Miscellaneous Power Repairs — ^Buildings " — Machinery and Plant. Supplies Salaries Taxes Tools Expense 54.30 825.07 348.63 155.11 5466.20 5481.88 996.95 849.07 49441.31 1846.64 .47 .23 1.45 .42 1.05 .16 26.88 .03 .49 .21 .09 3.27 3.28 .60 .51 29.57 1.11 65451.27 39.14 Selling and General Expense : — Advertising Bad Debts written off Bossing Catalogues Commission ... 3877.88 246.33 1283.03 1148.35 2310.44 Depreciation 1778. 84 Labor 5114.16 Miscellaneous 903 . 26 Office Supplies 848.62 Postage 688.34 Salaries 8683.89 Telephones and Telegrams 647 . 53 Traveling 639.74 Special 1211.76 Interest Paid. . . . Profit for Peroid. 29382.17 2588.82 18499.15 2.32 .15 .77 .69 1.38 .06 .06 ..54 .51 .41 .19 .39 .38 .72 17.57 1.55 11.06 167209.36 100.00 Illustration No. S shows the ratio 35 items of cost bear the net sales of $167209.36. To divide these items of cost by 167209 and demonstrate the correctness of the same would occupy an expert 2 hours at the very least. They were worked on an adding machine, by an operator who has only used the machine for a few weeks, in less than 10 minutes. The following method was employed and gives absolutely correct results: The table of equivalents gives up to 10000 only. In this example we want to find the ratio the various items bear to 167209. As we can only use 4 figures, we find the equivalent of 1672. By ignoring the cents and the units of the dollars and multiplying by the remainder we find the results as given. In the first item we multiply the equivalent for 1672 (which is .0005980861) by 4944, 2nd by 185 (because it is 184.6, 3rd by 79, 4th by 38, 5th by 243 and so on. These illustrations will give an idea of the vast amount of time saved and the accuracy obtained in using the within tables. Further instructions and advice in the use of these equivalents in any parti- cular line of work will gladly be furnished upon request free of cost. THE FOLLOWING PAGES GIVES THE EQUIVALENTS OF NUMBERS FROM 1 TO 10,000 100 ds 200 ds 300 ds 400 ds 0. . 010000000 005000000 003333333 002500000. . 1 . i.OOOOOOOOO 009900990 004975124 003322259 002493766. . 1 2 .. .500000000 009803922 004950495 003311258 002487562. . 2 3 . . .333333333 009708738 . . . .004926108 003300330 002481390 . 3 4 . . .250000000 . . . .009615385 004901961 003289474 002475248 . . 4 5. ..200000000 009523810 004878049 003278689 002469136. . 5 6. .166666667 . . ..009433962 004854369 003267974 002463054. . 6 7 . . . 142857143 . . . .009345795 004830918 . . . .003257329 002457002 . . 7 8 . . .125000000 . . . .009259259 . . . .004807692 003246753 002450980 . . 8 9. ..111111111 009174312 004784689 003236246 002444988. . 9 10. .010000000 009090909 004761905 003225806 002439024 .. 10 11. .090909091. . ..009009009 004739337 003215434 002433090. .11 12 .. .083333333 . ...008928571 004716981. ...003205128. .. .002427184 .. 12 13. ..076923077 . . ..008849558 004694836 003194888 002421308. .13 14. .071428571 008771930 004672897 003184713 002415459. .14 15. .066666667 008695652 004651163 003174603 002409639 .. 15 16. .062500000. . ..008620690 004629630 003164557 002403846. .16 17. . .058823530. . . .008547009 004608295 . . . .003154574 002398082. . 17 18. .055555556 008474577 004587156 003144654 002392344. .18 19. . .052631580. . . .008403361 004566210 003134796. . . .002386635. . 19 20. ..050000000 008333333 004545455 003125000 002380952. .20 21. .047619048 008264463 004524887 003115265 002375297. .21 22. .045454545 008196721 004S04505. . ..003105590 002369668. .22 23. .043478261 008130081 004484305 003095975 002364066. .23 24. .041666667 008064516. . .004464286 003086420 002358491. .24 25 . . .040000000 008000000 004444444 003076923 002352941 . .25 26. .038461538 007936508 004424779 003067485 002347418. .26 27 .037037037 007874016 004405287 003058104 002341920. .27 28. .035714287 007812500 004385965 003048780 002336449. .28 29. ..034482760. . ..007751938 004366812 003039514 002331002. .29 30 . . .033333333 007692308 004347826 003030303 002325581 . . 30 31 . . .032258065 . . . .007633588 004329004 003021148 002320186. .31 32. .031250000 007575758 004310345 003012048 002314815. .32 33. .030303030 007518797 004291846 003003003 002309470. .33 34. .029411765 007462687 004273504 002994012 002304148. .34 35 . . .028571429 . . . .007407408 004255319 002985075 002298851 . .35 36. .027777779. ...007352941. ...004237288 002976190.. .002293579. .36 37 . . .027027029 007299270 0042 19409 002967359 . . . .002288330 . . 37 38. ..026315790 007246377 004201681 002958580 002283105. .38 39. .025641027 007194245 004184100 002949853. . .002277905. .39 40. ..025000000 007142857. ..004166667 002941176 002272728. .40 41 . . .024390244 007092199 004149378 002932551 . . . .002267574. .41 42 . . .023809524 . . . .007042254 . . . .00413223 1 002923977 . . . .002262444 . . 42 43. .023255814 006993007. . ..004115226 002915452 002257337. .43 44. .022727273 006944444 004098361 002906977 002252253. .44 45. ..022222222 006896552 004081633 002898551 002247192. .45 46. . .021739130 006849315 004065041 002890173 002242153 . .46 47 . .021276596. . .006802721 004048583 002881844 002237138. .47 48, ..020833334 006756757 004032258 002873563 002232144. .48 49. .020408164. . ..006711410 004016064. . ..002865330 002227173. .49 Coutiuued on Opposite Page 100 ds 200 ds 300 ds 400 ds 50 . . .020000000 006666669 004000000 002857143 002222222 . , SO 51 . . .019607843 006622519 003984065 002849003 . . . .002217296 . . 51 52. ..019230769. . ..006578949 003968255. . ..002840909 002212390. .52 53. ..018867925 006535950 003952570 002832862 002207506. .53 54. ..018518519 006493509 003937009 002824860 002202644. .54 55. ..018181819 006451615 003921570 002816902 002197802. .55 56. . .017857143 006410260 003906251 . . . .002808990 002192984 . . 56 57. ..017543860 006369429 003891052 002801121 002188186. .57 58. ..017241380 006329117 003875971 . . ..002793299 002183407. .58 59. ..016949153 006289310. . ..003861005 002785517 002178650. .59 60. ..016666667 006250000. . ..003846155 002777779 002173913 . .60 61. ..016393443 006211181 003831419 002770084 002169199. .61 62. ..016129032 006172840 003816796 002762431 002164502. .62 63 . . .015873016 006134971 003802283 . . . .002754821 . . . .002159828 . . 63 64 . . .015625000 006097564 003787880 002747254 002155173 . . 64 65. ..015384616 006060609 003773588 002739728 002150539. .65 66. ..015151516 006024100 003759400 002732241 002145923. .66 67. ..014925373 005988028 003745320 002724799 002141329. .67 68. ..014705883 005952388 003731346 002717394 002136753. .68 69. ..014492754 005917165 003717476 002710029 002132199. .69 70. ..014285714 005882355 003703705 002702703 002127660. .70 71. ..014084507 005847956. . ..003690039 002695419 002123143. .71 72. ..013888889 005813957 003676471 002688173 002118645. .72 73. ..013698630 005780349 003663005 002680967 002114166. .73 74. .013513514 005747129 003649637 002673799 002109705. .74 75. ..013333334 005714290 003636366 002666669 002105264. .75 76. ..013157895 005681820 003623190 002659577 002100841. .76 77. ..012987013 005649720 003610110 002652520 002096438. .77 78. ..012820513 005617982 003597124 002645503 002092051. .78 79. ..012658228 005586599 003584230 002638524 002087685. .79 80. ..012500000 005555559. . ..003571430 002631580 002083334. .80 81. ..012345679 005524864 003558720 002624673 002079002. .81 82. ..012195122 005494509. . ..003546461 002617801 002074690. .82 83 . . .012048193 005464484 003533570 . . . .002610968 002070395 . . 83 84. ..011904762. . ..005434788 003521129 002604169 002066117. .84 85. ..011764706 005405409 003508774 002597403 002061857 .85 86 . . .01 1627907 005376349 003496505 . . . .002590676 002057614 . . 86 87. ..011494253 005347599 003484321.. ..002583981 002053390. .87 88. ..011363637 005319152 003472224 002577320 002049182. .88 89. ..011235956 005291009 003460209 002570698 002044992. .89 90... 011111111 005263160. ...003448278 002564103. . . .002040818. .90 91. ..010989011 005235604 003436429 002557546 002036660. .91 92. .010869565 005208337 003424659. . ..002551021 002032520. .92 93. ..010752688. . ..005181350 003412970 002544530. . ..002028399. .93 94. ..010638298 005154640 003401362 002538072 002024293. .94 95. ..010526316 005128209 003389831 002531648. . .002020202. .95 96 ..010416667 . . ..005102044 003378380 002525254 002016130. .96 97. ..010309279. 005076147 003367005 002518894. . .002012074. .97 98. . .010204082 005050509 003355706 002512565 002008033 . .98 99 . . .010101010 005025129 003344486 002506269 . . . .002004009 . . 99 500 ds 600 ds 700 ds 800 ds 900 ds 0. .002000000 001666667 001428571 001250000 001111111. . 1. ..001996008 001663894 001426534 001248439 001109878. . 1 2 .001992032. ...001661130.. ..001424501 001246883 001108648. . 2 3 .001988072 001658375 001422475 00124.5330 001 107420 . . 3 4. . .001984127 . . . .001655629 001420455 001243781 001106195. . 4 5 . . .001980199 001652893 001418440 . . . .001242236 001 104973 . . 5 6. .001976286. . ..001650166 001416431 001240695 001103753. . 6 7. .001972388. . .001647447 001414427 001239158 001102536. . 7 8 . . .001968504 . . . .001644737 001412430 001237624 001 101322 . . 8 9. ..001964637. . ..001642037.. ..001410438 001236095 001100110.. 9 10 . . .001960784 001639344 001408451 . . . .001234568 001098901 . . 10 11. .001956947. . ..001636661 001406470 001233046 001097695. .11 12. .001953125 001633987 . . ..001404495 001231527 001096491 .. 12 13 . . .001949318 001631321 001402525 . . . .001230012 001095291 . . 13 14. .001945526 001628665 001400561 . . ..001228501 001094092. .14 15. ..001941748 001626016 001398601 001226994 001092897. .15 16. .001937986 001623377 001396649 001225491 001091703. .16 17. .001934237 001620746 001394700 001223991. . .001090513. .17 18. ..001930502. . .001618123 001392758 001222495 001089325. .18 19. .001926784 001615509 001390821 001221001 001088140. .19 20. .001923077 001612903 001388889. . ..001219512 001086957. .20 21. .001919386 001610306 001386963 001218027 . . .001085777. .21 22. .001915709 001607717 00138S042 001216545 001084599. .22 23. .001912046. .001605137. . ..001383126 001215067 001083424. .23 24. .001908398 001602565 001381215. . .001213593 001082251. .24 25. .001904763. .001600000.. .001379310.. .001212121 001081082. .25 26. .001901141 001597445 001377411 001210654 001079914. .26 27. ..001897534 001594898 00137SS16 001209191 001078749. .27 28. .001893940 001592358 001373627 001207730 001077587. .28 29. .001890360 001589826. . ..001371743 001206273 001076427. .29 30. .001886793 001587302 001369863 001204819 001075269. .30 31. ..001883239 001584786 001367989. . ..001203370 001074114. ,31 32. ..001879700 001582279 001366120 001201923 001072962. .32 33. .001876173 001579779 001364257 001200480 001071811. .33 34. ..001872660 001577288 001362399 001199041 . . .001070664. .34 35. .001869160 001574803 001360545 001197605 001069519. .35 36. .001865673 001572328 001358697 001196173 001068377, .36 37 .001862199 001569860 001356853 001194744 001067236. .37 38. ..001858737 001567399. . ..001355014 001193318 001066099. .38 39. .001855289 001564946 001353181. . ..001191896 001064963. .39 40. .001851852 001562500 001351351 001190476 001063830. .40 41. ..001848429 001560063 001349528. . ..001189061 001062699. .41 42. .001845019 001557633 001347709. . ..001187649. . .001061571. .42 43 . . .001841621 001555210 001345896 , . . .001186240 001060446. .43 44. .001838236 001552796 001344087 001184834. . ..001059322. .44 45. .001834863 001550389 001342283 001183432 001058201. .45 46. .001831502. . .001547989 001340483 001182033 001057083. .46 47. ..001828155 001545597 001338689 001180638 001055967. .47 48. ..001824818 001543210 001336899. . ..001179246 001054853. .48 49. .001821496 001540833 001335114 001177857 . . , .001053741 . .49 Continued on Opposite Page 500 ds 600 ds 700 ds 800 ds 900 ds 50. .,001818182 001538462 001333334 001176471 001052632 .. 50 51 .. .001814882 001536099 001331559 001175089 001051525 . .51 52. ..001811595 001533743 001329788 001173709 001050420. .52 53. ..001808319 001531394 001328021 001172333 001049318. .53 54. ..001805055 001529052 001326260 001170960 001048219. .54 55. ..001801802 001526718 001324504 001169591 001047121 . .55 56. ..001798562 001524391 001322752 001168225 001046021 . .56 57. ..001795333 001522071 001321004 001166861 001044932 . .57 58. ..001792115. . ..001519758 001319262 001165501 001043842. .58 59. ..001788909. . ..001517451 001317524 001164145 001042754. .59 60. ..001785715 001515152 001315790 001162791 001041667 . .60 61. ..001782531 001512860 001314061 001161440. . .001040583. .61 62. ..001779360 001510575 001312337 001160093 001039501. .62 63. ..001776200 001508297 001310617 001158749 001038422. .63 64. ..001773050 001506025 001308901 001157408 001037345. .64 65. ..001769912. . ..001503760 001307190 001156070. . .001036270. .65 66. ..001766786 001501502 001305484 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