Manual / Guide · c. 1964

Friden 130 Electronic Calculator Instruction Manual

The 52-page operator's manual for the EC-130: the keyboard, the four-register stack, ENTER and REPEAT, decimal setting, and worked examples.

Author: Friden, Inc.
Year: c. 1964
Type: Manual / Guide
Credit: Scan: Rick Bensene, Old Calculator Web Museum, oldcalculatormuseum.com.

← Back to the Reference Library

Be alectronic Calculator Instruction Manual Price $2.00 Friden, Inc. . Educational Center Published by 31 Prince Street Rochester, New York 14607 OPERATING INSTRUCTIONS FOR Friden 130 Electronic Calculator Copyright 1964 by Friden, Inc. *A Trademark of FRIDEN, INC. FOREWORD Operating the Friden Electronic Calculator 130 is like stepping into a new world of computing power for the desk calculator user. Through the magic of electronics, the features of storage capacity, flexibility, speed, silence, and decimal control are advanced to a level never before attained. Designed to meet the styling requirements of modern business, the Friden 130 is a pleasant complement to any office decor. The complete operating silence of this machine eliminates disturbance of office personnel and promotes efficiency. This machine is a solid-state device. These non-moving components are the secret to high-speed calculation. Input amounts and results of operation are visible instantly on the face of a cathode ray tube after the entry or function key is operated. Intermediate results are automatically retained in the upper registers. Also, an amount or result may be stored for further use in a memory unit. A feather-touch eleven-key keyboard provides the means for numerical input. Function keys placed adjacent to this section are arranged for operator convenience and ease of operation. Accuracy in decimal point control is insured by a fixed point system, around which all input amounts and results are automatically aligned. No other programming is nec- essary. The decimal point location can be manually selected for five different operating situations according to the requirements of the work at hand. The 130 Electronic Calculator is able to handle a wide range of business and scientific applications in a logical and direct manner. The high degree of flexibility permitted in approaching problems makes this machine highly adaptable to arithmetic calculations of great variety. TABLE BASIC OPERATIONS Register Display Keyboard Operating Controls Addition /Subtraction Multiplication Without Decimals . With Decimals Accumulation of Products Positive Negative... Chain Multiplication Division Without Decimals . With Decimals .... . Lo Addition of Quotients .... . Addition/Subtraction of Quotient: Squaring a Number Without Decimals. . . Accumulative Squaring Negative Squaring a Calculating Algebraically. . . . . Sequential Operations The Memory Unit Raising to a Power Loe Accumulation of Products/Multipliers Problems Involving Two Constants BUSINESS APPLICATIONS Invoicing Lol. Individual/Accumulated Percentages Percentage Problems Simple and Compound Interest . . OF CONTENTS ow NY Fe for) for) ee en | oOo © CO oOo 10 11 12 13 14 15 16 .. 17 18 Interest Rate on Installment Loans Equal Monthly Payments Installment Payments on Mortgages . MISCELLANEOUS APPLICATIONS Probability... . Actuarial Problem... ....... Probability —Life Insurance Geometric Series Standard Deviation . ENGINEERING APPLICATIONS Volume of a Sphere Conversion of Denominate Numbers . Area of a Sector Interpolation . . . Evaluating an Integral . . Evaluating a Polynomial Method #1 Method #2 Determinants. . Cosine Law Square Root Cube Root . . . Overcapacity Problems Double Precision Multiplication. . . Index CHARTS AND TABLES 1941 Commissioners Standard Ordinary Mortality Table Tangents and Cotangents Cube Root Table 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 36 38 40 42 43 45 24 30 40 Friden 130 Electronic Calculator REGISTER DISPLAY The Friden 130 Electronic Calculator employs a new concept in computation. Commonly referred to as the ‘‘stacking”’ principle, it permits automatic storage of intermediate answers for later usage, according to the requirements of the formula being solved. Four 13-digit registers are arranged in a stack as follows: 1. WORKING REGISTER (#1). The bottom register is known as the Working Register. All entries and answers appear in it. All numbers enter the Display through this register and are displaced upwards as subsequent entries are made. 2. REGISTER #2. One number of an arithmetic operation appears in this register, the other appears in the Working Register. When, how- ever, the two terms appearing in these registers are combined arithmetically (added, subtracted, multiplied, or divided) the answer appears in the Working Register. Any values which were in the 3rd and 4th registers automatically shift down one position. . REGISTERS #3 and #4. These registers are used for storage of intermediate answers. This ‘“‘stack” of four registers, then, fills and empties from the bottom on a “‘first in, last out’’ basis. If a fifth entry is made with all registers full, the contents of Register #4 ‘‘overflow”’ off the top and are lost. HA Las = — 171826934SIi2le #9 ——: 9000218631449 wee ggg00041 551.36 KEYBOARD AND OPERATING CONTROLS DECIMAL POINT 1. Over-Flow Lock 2. Clear Entry Key 3. Change Sign Key 4. Enter Key 5. Repeat Key 6. Division Key 7. Multiplication Key 15. Clear All 10. 11. 12. 13. 14. Keyboard Decimal Point Key Plus Key Recall Key Minus Key Store Key Decimal Point Selector OPERATING 1. OVER-FLOW LOCK KEY-—TIf a number, en- tered in Working Register #1, is beyond the left of decimal capacity of the selected decimal point pro- gram, the OVER-FLOW LOCK signal lights up. For example, if the Decimal Point Selector is set on “7” it would mean that six digits only, can be indexed in the keyboard to the left of the decimal point. (13 digits capacity minus 7 decimal places equals 6 digits to the left of decimal.) If then 1,234,567.89 is indexed on the keyboard, the OVER-FLOW LOCK signal lights up upon depression of the ENTER key. There is one other situation in which the OVER- FLOW LOCK signal lights up. That is, where an answer exceeds the number of digits to the left of the selected decimal point program. Once the over-flow signal light is on, all keys are locked to prevent further usage. Touching either the CLEAR ENTRY or CLEAR ALL keys will turn off the signal, unlock the keyboard, and simul- taneously clear the affected registers. The key- board may also be unlocked merely by touching the OVER-FLOW Lock key itself. A Decimal Interlock is provided to prevent over- loading digits to the right of the decimal point. Assuming a decimal selection of 2, then only two digits can be indexed after the decimal point key is depressed. The third and subsequent digits are automatically disregarded. 2. CLEAR ENTRY—A touch of the CLEAR ENTRY key will clear Working Register #1. If a mistake is made in indexing a number, touch the CLEAR ENTRY key and proceed with the problem. 3. CHANGE SIGN Key—This key will permit calculations with algebraic sign changes. As an example take the problem 23.45— (—.895). Use of the CHANGE SIGN key permits entry of .895 CONTROLS into the Working Register with the negative sign attached. The resultant answer will appear with the correct sign. See page 9 for other examples of this feature. 4, ENTER KEY—When a number is indexed in the keyboard that number appears immediately in Working Register #1—but without the decimal point. A touch of the ENTER key, then, decimally aligns it. All function keys cause decimal align- ment also. Therefore, when using such keys as CHANGE SIGN, REPEAT, and RECALL, it is not necessary to touch the ENTER key first. 5. REPEAT Key—The REPEAT key duplicates the contents of Register #1 in Register #2. The most common applications utilizing this feature are those involving squaring. But the REPEAT key may be used equally well for problems involv- ing discounts, commissions, chain discounts and compound interest, to name a few. Squaring is a three step operation: (1) Index the number (2) Touch the REPEAT key, (3) Touch the Multipli- cation (x) key. 6. DIVISION Key—A touch of the Divide key will cause the contents of Register #2 to be di- vided by the contents of Register #1. The answer will appear, decimally aligned in Register #1. To divide, the procedure is as follows: (1) Index the dividend (2) Touch ENTER key (8) Index the divisor (4) Touch the Divide (+) key. If the Divide key is depressed with nothing in the Working Register, the Display goes blank and the machine will run indefinitely in the process of division. Touch the CLEAR ALL key to restore the Display. 7. MULTIPLICATION Key—A touch of the MULTIPLICATION key will cause the contents of Register #1 to be multiplied by the contents of i { DECIMAL POINT (cen strennnmengr marta Register #2. The product will appear, decimally aligned, in Register #1. To multiply, the pro- cedure is as follows: (1) Index the multiplicand (2) Touch ENTER key (3) Index the multiplier (4) Touch the Multiplication (x) key. 8. KEYBOARD—AIi numbers are indexed on the “‘11-key”’ keyboard. The “11th” key is a decimal point key. As a number is indexed on the keyboard it appears in Register #1, digit by digit from the right. 9. DECIMAL POINT Key—The Decimal Point key must be depressed whenever a number with a decimal point in it is indexed in the keyboard. If the Decimal Point key is not used, the machine accepts the entry as a whole number. So 456.78 is indexed as 4-5-6-decimal point-7-8. And 678 is indexed as 6-7-8; the Decimal Point key need not be depressed in this case. 10. PLUS Key—A touch of the PLUS key will cause the contents of Register #1 to be added to the contents of Register #2. The answer will appear, decimally correct, in Register #1. To add, the procedure is as follows: (1) Index first number (2) Touch ENTER key (38) Index next number (4) Touch PLUS (+) key. Repeat steps #3 and 4 for subsequent numbers. 11. RECALL Key—The RECALL Key recalls any number stored in the Memory Unit. The number stored may be repeatedly recalled to Register #1 for subsequent operations. 12. MINUS Key—A touch of the MINUS key will cause the contents in Register #1 to be sub- tracted from the contents of Register #2. The answer will appear, decimally correct in Register #1. To subtract, the procedure is as follows: (1) Index the first number (2) Touch ENTER key (3) Index the second number (4) Touch the MINUS (-—) key. 13. STORE Key—A fifth register, not displayed, is provided for storage of a constant. A touch of the STORE key will transfer a number from Register #1 to the Memory Unit. If a number is already in storage, it replaces the old number with the new one. The stored number may be recalled as often as desired. 14. DECIMAL POINT SELECTOR— Automatic decimal control is maintained in all registers in keeping with the number of decimal places indi- cated on the decimal programs control wheel. There are five different decimal programs avail- able. These are 0, 2, 5, 7, and 13. To eliminate needless shifting of the Decimal Point Selector, most problems in this manual are worked over a 5 place decimal program. 15. CLEAR ALL Key—A touch of the CLEAR ALL key clears all registers—including the Memory Unit. ADDITION/ SUBTRACTION GENERAL INSTRUCTIONS 1. An ON/OFF switch is located under the lower right corner of the calculator. Push the lever back, in order to turn the machine on. The Display will appear in a few seconds. . Numbers are indexed in the 11-key keyboard just as they are written. . If an error is made in indexing a number, touch CLEAR ENTRY and begin over again. PROBLEMS: 1. Addition without Decimals................ 2. Addition with Decimals................... 3. Subtraction with True Credit Balance....... 4, Addition and Subtraction.................. 5. Subtracting Algebraically.................. 4. The DECIMAL POINT key is used in all cases—except for whole numbers. For example, 28.13 is entered as 2-8-decimal-1-3; the number 68 is entered as 6-8; the decimal point is not required. . Since all entries are positive, a CHANGE SIGN key is provided to make these entries negative, when necessary. See example #5 below. . Clearing is unnecessary between problems. 68 + 93 = 161 28.138 + 17.24 = 45.37 97.24 — 118.43 = —21.19 15.243 + 17.819 — 23.147 = 9.915 22.43 — (—32.46) = 54.89 INDEX IN TOUCH CONTROL KEYS SOLUTION KEYBOARD IN SEQUENCE Note: Move Decimal Point Selector to position 1. 68 + 93 = 161.00000 68 ENTER 93 2. 28.138 + 17.24 = 45.37000 28 013 ENTER 17024 3. 97.24 — 118.48 = 21.19000— 97 24 ENTER 118 043 [=] 4. 15.248 + 17.819 = 33.06200 15 0243 ENTER 174819 33.062 — 23.147 = 9.91500 230147 =] 5. 22.43 — (—32.46) = 54.89000 22 43 [ENTER] 32046 [CHANGE SIGN] [=] MULTIPLICATION PROBLEMS: 1. Multiplication without Decimals.................. 12 x 24 = 288 2. Multiplication with Decimals..................... 24.02 X .9401 = 22.5812 3. Accumulation of Products Positive... 00. eee eee (39.445 & 15.2) + (41 X .6) = 624.164 Negative... 00.00 eee eee (8 xX .14) — (.007 x 21) = .273 4. Chain Multiplication............0.....00....000.. 23.8 X 16.92 X .708 = 285.10876 INDEX IN TOUCH CONTROL KEYS SOLUTION KEYBOARD IN SEQUENCE Note: Move Decimal Point Selector to position 1.12 X 24 = 288.00000 12 ENTER 24 2. 24.02 * .9401 = 22.58120 24 02 ENTER 9401 3. 39.445 X 15.2 = 599.56400 39 e445 ENTER 1502 599.564 + (41 X .6) = 624.16400 Al ENTER 26 3 X .14 = .42000 3 ENTER ol4 A2 — (007 X 21) = .27300 2007 ENTER 21 [=] 4. 23.8 X 16.92 = 402.69600 23 28 ENTER 16.92 402.696 X .708 = 285.10876 0/08 DIVISION PROBLEMS: 1. Division without Decimals...................0....0... 145 + 12 = 12.08333 2. Division with Decimals................0.....0 00000008 4,962.184 + 13.2 = 375.92303 8. Addition of Quotients............0 00.00.0005 00 000. e eee = + ee = 64.63829 ey: . . 45 34.26 17.76 4. Addition/Subtraction of Quotients..................... 3 + 121 7 3195 ~ 12.14820 INDEX IN TOUCH CONTROL KEYS SOLUTION KEYBOARD IN SEQUENCE Note: Move Decimal Point Selector to position 1.145 + 12 = 12.08333 145 ENTER 12 [=] 2. 4,962.184 + 13.2 = 375.92303 4962 0184 ENTER 1342 [=] 624 3. 3 = 48.00000 624 ENTER 13 El 78.2 7 = 64.63829 718 02 ENTER 407 ] 45 4, 37 15.00000 45 ENTER 3 [=] 34.26 21 = 17.83140 34026 ENTER : 1241 F 17.76 ~ 3495 7 12.14820 17076 ENTER 30125 AA SQUARING A NUMBER PROBLEMS: 1. Accumulative Squaring without Decimals. ...............0..00005. 25? + 12? = 769 2. Accumulative Squaring with Decimals.. 78.23? + 26.352 = 6,814.25540 3. Negative Squaring................... 34.1262 — 18.29? = 830.05977 4. Accumulative/Negative Squaring... ... 18.124? + 9.182 — 15.232 — 3.14162 = 170.92922 INDEX IN TOUCH CONTROL KEYS SOLUTION KEYBOARD IN SEQUENCE : Note: Move Decimal Point Selector to position 1. 252 = 625 25 REPEAT +12? = 769 12 REPEAT 2. 78.23? = 6119.9329 78023 REPEAT +26.352 = 6,814.25540 26 035 REPEAT 3. 34.126? = 1,164.58387 340126 REPEAT —18.292 = 830.05977 18429 REPEAT [=] 4. 18.1242 = 328.47937 180124 REPEAT + 9.182 = 412.75177 9018 REPEAT —15.232 = 180.79887 15 023 REPEAT [=| — 3.14162 = 170.92922 301416 REPEAT [=] CALCULATING ALGEBRAICALLY PROBLEMS: 1. Minus + Minus................. (—147.12) + (—13.67) = 10.76225 2. Plus X Minus x Minus.......... 14.25 x (—8.69) X (—2.63) = 325.67947 3. (Minus + Plus) — (Plus + Minus) [(—278.35) + 9.035] — [843.7 + (—28.001)] = —.6769 4. Plus x Minus + Minus.......... (97.14 X (—8.754)] + (—2.345) = 362.62838 INDEX IN TOUCH CONTROL KEYS SOLUTION KEYBOARD IN SEQUENCE Note: Move Decimal Point Selector to position —147.12 1. —Tg67 7 10-76225 147012 [CHANGE SIGN| 13067 [CHANGE SIGN] [=] 2.14.25 X (—8.69) = —123.83250 14.25 8 269 [CHANGE SIGN] X (—2.63) = 325.67947 2063 [CHANGE SIGN| — 278.35 3. Fogg ~~~ 30-80796 278.035 [CHANGE SIGN] 9 2035 [=] 843.7 —30.80796 — (Seo) = —.67690 84307 28 001 [CHANGE SIGN] [=] [=] 4. 97.14 X (—8.754) = —850.36356 97014 80754 | CHANGE SIGN] TSPO SESS = 362.62838 20345 [CHANGE SIGN] [=] 2.345 ~ - ° SEQUENTIAL OPERATIONS PROBLEMS: 1. (27.634 X 8.13) + 23.45 = 9.58057 2. (12.3 + 6.78) x 9.84 x 7.642 = 1347.93714 14.2 — 6.07 347.9 3. 164 31 * (1.4)3 3 7 = 1.84547 > xX 4.7 X .89 2 INDEX IN TOUCH CONTROL KEYS SOLUTION KEYBOARD IN SEQUENCE Note: Move Decimal Point Selector to position 1. 27.634 X 8.13 = 224.66442 27 2634 ENTER 8013 224.66442 + 23.45 = 9.58057 23 045 [=] 2.12.3 + 6.78 = 19.08 12.3 ENTER 6678 -F| 19.08 X 9.84 = 187.74720 9084 [x] 187.74720 X (7.64)? = 10,958.72896 764 [REPEAT] 14.2 ENTER Divide by (14.2 — 6.07) = 1347.93714 6.07 [=] [=] 3. 164 + 13.1 = 12.51908 164 [ENTER 1361 [=| Multiply by (1.4)? = 34.35235 104 REPEAT] [REPEAT | 8.9 +2 = 4.45 89 [ENTER 2 +] 4.45 X 4.7 = 20.915 407 20.915 X .89 = 18.61435 89 34.35235 18.61435 — 13447 E] 10 THE MEMORY UNIT GENERAL To enter a number into the Memory Unit, index that number into the keyboard and touch the STORE key. To recall the number from storage, touch the RECALL key. The number entered into storage remains there for subsequent usage. It will continue to remain there until the CLEAR 2. CONSTANT DIVISOR 145 + 12.13 = 11.95383 214 + 12.138 = 17.64220 846 + 12.138 = 69.74443 3. CONSTANT DIVIDEND ALL key is touched, or another number is entered 164 + 18.92 = 8.66807 into storage. 164 + 24.16 = 6.78807 164 + 2.013 = 81.47044 PROBLEMS: 1. CONSTANT MULTIPLIER $1.25 X 21 = 26.25 1.25 x 64 = 80.00 1.25 x 182 = 227.50 Note: Move Decimal Point Selector to position 1.1.25 X 21 = 26.25 1625 21 * 1.25 X 64 = 80.00 64 1.25 X 182 = 227.50 182 2.145 + 12.13 = 11.95383 145 12013 [STORE ][RECALL] [=] 214 + 12.13 = 17.64220 214 [+] 846 + 12.13 = 69.74443 846 [+] 3. 164 + 18.92 = 8.66807 164 [ STORE ||RECALL| 18.92 [=| (Observe Answer) 164 + 24.16 = 6.78807 24016 [=] (Observe Answer) 164 + 2.013 = 81.47044 22013 [=] (Observe Answer) *Depression of the RECALL key will cause decimal alignment of the indexed number and recall of the constant from memory in one operation. 11 RAISING PROBLEMS: 1. 85 = 32,768 2. Same problem; alternate method 3. (1.02)39 = 1,8113602 Law of Exponents A number may be easily raised to any power by employing the ‘‘Laws of Exponents.”’* The follow- ing laws are valid where m and n are any integers (positive, negative, or zero). TO A POWER 1. To multiply, add exponents. am X an = a(mtn) 2. To divide, subtract exponents. am + an = a(m—n) 3. To raise a power to a power, multiply exponents. ( am) n = qmn 4, The power of a product is the product of the powers. (a b)= = anbn 5. A power of a quotient is the quotient of the powers. a\n _ an (5)" Bs INDEX IN TOUCH CONTROL KEYS SOLUTION KEYBOARD IN SEQUENCE Note: Move Decimal Point Selector to position = 1.85 82 = 64 8 [REPEAT] [STORE | [RECALL | [x] 83 = 512 RECALL 84 = 4,096 “ “ 85 = 32,768 “ « 2 82 = 64 8 [REPEAT] [REPEAT] 84 = 4,096 REPEAT 85 = 32,768 3. (1.02)? = 1.0404 1.02 [REPEAT] |x| | STORE ||RECALL (1.02)4 = 1.0824321 REPEAT (1.02)8 = 1.1716592 “ “ (1.02)!® = 1.3727852 “ “ (1.02)32 = 1.8845392 « «“ (1.02)32 + (1.02)2 = (1.02)39 = 1.8113602 RECALL] [=| *From G. James and R. C. James, Ed.. MATHEMATICS DICTIONARY. Copyright 1949, 1959, D. Van Nostrand Co., Inc., Princeton, New Jersey. 12 ACCUMULATION OF PRODUCTS/MULTIPLIERS Read © X (80) in Register #2 Read = X? (1290) in Register #1 PROBLEMS: 2.X% xX? 14 196 1. 64 x 44 = 2816 15 295 27 X 56 = 1512 16 256 28 Xx 66 = 2470 17 289 129 6798 18 324 80 1290 FIND: =X = _ 80 =X2 = 1290 Note: Move Decimal Point Selector to position 1.64 X 44 = 2816 64 a 27 X 56 = 1512 27 [REPEAT] 56 [<] [RECALL] [+][ STORE] 388 X 65 = 6798 38 |REPEAT 65 [RECALL] [+][STORE] The sum of the products (6798) appears in Register #1. The sum of the multipliers (129) appears in Register #2. 2. 142 = 196 14 [REPEAT] [REPEAT] |x] |STORE + 152 = 421 15 [REPEAT] [REPEAT] [RECALL] [+] [STORE] + 162 = 677 16 Same as step #2 +172 = 966 17 Same as step #2 + 182 = 1290 18 Same as step #2 13 PROBLEMS INVOLVING TWO CONSTANTS PROBLEMS: 1. (Ki X 0.95) + (Ko X 0.65) = 25.345 K, = 145 2. (Ki X 0.85) + (Ka X 0.55) = 22.115 Ky = 17.8 3. (Ki X .78) + (Ke X 0.56) = 21.278 INDEX IN TOUCH CONTROL KEYS SOLUTION KEYBOARD IN SEQUENCE Note: Move Decimal Point Selector to position 1. Store K; 1465 REPEAT] * Store Ko 178 STORE (14.5 X 0.95) = 18.775 095 + (17.8 X 0.65) = 25.345 265 RECALL 2. Clear previous answer |CLEAR ENTRY| |REPEAT| (14.5 X 0.85) = 12.325 85 + (17.8 X 0.55) = 22.115 055 RECALL 3. Clear previous answer [CLEAR ENTRY| |REPEAT| (14.5 X 0.78) = 11.31 °78 + (17.8 X 0.56) = 21.278 256 RECALL *The REPEAT key causes duplication of the contents of Working Register #1 in Register #2. The lower value may be used for a first operation. The upper value will be carried for subsequent usage. 14 INVOICING PROBLEM: 14 lbs. @ $.56 lb. = $ 7.84 23 lbs. @ .571b. = 18.11 40 ft. @ 62ft. = 24.80 Sub Total 45.75 Add: 3% Sales Tax 1.37 Total $47.12 (14 X .56) = 7.84 + (23 X .57) = 20.95 + (40 X .62) = 45.75 (45.75 X .03) + 45.75 = 47.12 14 056 23 057 062 203 Note: Move Decimal Point Selector to position & a ENTER + Ix) [+] ENTER + El fg] & kg A |g! | key instead of the Plus key. NOTE: If the problem had called for a 3% discount instead of a 3% sales tax, the final step would be to touch the Minus INDIVIDUAL/ACCUMULATED PROBLEM: DEPT. SALES % A $ 6845 19.27 B 15322 43.13 C (5537) (15.59) D 6431 18.10 E 16275 45.82 F (1548) (4.35) * G (2265) (6.38) 35523 100.00 *Adjusted for .01 INDEX IN TOUCH CONTROL KEYS SOLUTION KEYBOARD IN SEQUENCE Note: Move Decimal Point Selector to position 35523 STORE 6845 + 35523 = .19269** 6845 RECALL [=] 15322 + “ = .43132 15322 “ “ (5537)+ “ = .15587 5537 “ « (-] 6431 + “ = .18103 6431 “ “ 16275 + “ = .45815 16275 “ «4 (1548)+ “ = .04357 1548 “ 7“ [=| (2265)+ “ = 06376 2265 “ «« **NOTE: To convert from a decimal to a percent, it is necessary to multiply mentally by 100. 16 PERCENTAGE PROBLEMS PROBLEMS: 1. What % of $345.65 is $78.25? Answer: 22.638% 2. Increase or Decrease and Percent. Last year This year Change % Change 6375.85 7894.65 +1518.80 +23.82% 8765.45 3975.42 — 4790.03 —54.65% 3. Percent Mark-up on Selling Price Sell Cost Gross Profit Mark-up % $942.38 $656.75 $285.63 30.31% 325.60 234.65 90.95 27.93% INDEX IN TOUCH CONTROL KEYS SOLUTION KEYBOARD IN SEQUENCE NOTE: The number after the “‘of’’ in the problem is always the denominator. Note: Move Decimal Point Selector to position 1. 78.25 + 345.65 = .22638 = 22.638% 78 025 ENTER 345 065 [+] 2. 7894.65 — 6375.85 = 1518.80 7894 665 6375 85 [STORE |[RECALL] [=] 1580.80 + 6375.85 = .23821 = 23.821% RECALL] [+] 3975.42 — 8765.45 = —4790.03 3975 042 ENTER 8765 045 [STORE |[RECALL] [-] — 4790.03 + 8765.45 = —.54646 = —54.646% RECALL] [=] 3. 942.38 — 656.75 = 285.63 942 038 {STORE |} RECALL | 285.63 + 942.38 = .30309 = 30.309% 656075 [=] [RECALL] [=] 325.60 — 234.65 = 90.95 325 «60 [STORE |[RECALL} 90.95 + 325.60 = .27933 = 27.933% 234 665 [=] [RECALL] [=] 17 SIMPLE AND COMPOUND INTEREST PROBLEMS: 1. Compute the ordinary simple interest on a loan of $1700.00 at 534% for 92 days. Interest = (Principal x Rate x Days) /360 = ($1700.00 x .0575 x 92) + 360 = $24.98 2. Find the compound amount of $6,150.00 at 5% interest compounded quarterly for four years. 16 S =P( +i)" = 6150.00 (1 + va) = 6150 X (1.0125) 16 S = $7502.32 3. $1000.00 @ 6% compounded yearly for 12 years. 1000.00 x .06 x (1.06)!2 = $2012.20 Note: Move Decimal Point Selector to position 1. $1700.00 X .0575 = $97.75 1700 20575 97.75 X 92 = 8,993.00 92 8993.00 + 360 = 24.98055 360 [=] Note: Move Decimal Point Selector to position 2. Enter $6150.00 for later use 6150 (1.0125)? = 1.025 156 2 100125 (1.0125)* = 1.050 945 2 “ “ (1.0125)8 = 1.104 485 8 «“ “ (1.0125)1® = 1.219 888 8 “ “ 1.2198888 X 6150.00 = 7502.3161200 = $7502.32 3. Enter $1000.00 for later use 1000 (1.06)? = 1.1236 1.06 (1.06)4 = 1.2624769 (1.06)§ = 1.5938479 [REPEAT | [REPEAT | (1.06)4 X (1.06)8 = (1.06)!2 = 2.0121961 (1.06)!2 X 1000.00 = 2012.1961000 18 INTEREST RATE ON INSTALLMENT LOANS PROBLEM: A colored television set sells for $720.00 cash. If a buyer agrees to pay $240.00 cash and the balance in 10 equal monthly payments of $53.50 each, what rate of interest is he being charged? 72T R = Interest Rate per annum FORMULA:R = ORMUL 8A (n+ 1) + Tm —- 1) A = Amount of Loan 79 55.00 ($720.00 — 240.00 = $480.00) = SIO ~ BOO NS T = Total charge (10 x 53.50 — 480.00 = (3 x 480.00 x 11) + (95.00 x 9) $55.00) n = number of periods (10) INDEX IN TOUCH CONTROL KEYS SOLUTION KEYBOARD IN SEQUENCE Note: Move Decimal Point Selector to position 72T = 72 X 55.00 = 3960 72 55 3A = 3 X 480.00 = 1440 3 ENTER 480 3A(n + 1) = 1440 X 11 = 15840 11 + T (n — 1) = +(55.00 X 9) = 16,335 55 9 72T Sw PD i Te oD 2424 = 24.24% [=] 19 CREDIT LOANS DETERMINATION OF EQUAL MONTHLY PAYMENTS PROBLEM: A loan of $220.00 is to be repaid with interest at 214% per month for 12 months. Find the equal monthly payment. 1 i FORMULA: R = P : = P 1-—-(1+i)— 1 1 (1 +i)" .025 = (220.00) —_— z= $21.45 1 — (1.025) 12 INDEX IN TOUCH CONTROL KEYS SOLUTION KEYBOARD IN SEQUENCE Note: Move Decimal Point Selector to position 220.00 X .025 = 5.50 220 ENTER 2025 (1.025)2 = 1.05062 12025 REPEAT (1.025)4 = 1.1038 [REPEAT] [REPEAT| (1.025)8 = 1.21837 REPEAT (1.025)4 X (1.025)8 = (1.025)12 = 1.34483 STORE 1— 1.025) !2 = .25642 1 REPEAT RECALL] [+] [-] Monthly Payment = 21.44918 = $21.45 [=] 20 INSTALLMENT PAYMENTS ON MORTGAGES PROBLEMS: MONTHLY PAYMENT LOAN RATE PAYMENT INTEREST ON LOAN BALANCE 1. $3500.00 514% $45.00 $16.04 $28.96 $3471.04 2. $2275.25 5% 27.50 18.02 2257.23 ANALYSIS: Loan X Interest Rate per Annum = Interest Monthly Payment — Interest = Payment on Loan Loan — Payment on Loan = Balance of Loan Note: Move Decimal Point Selector to position 1. 3500.00 X .055 = 192.50 3500 0055 Interest = 192.50 + 12 = 16.04166 12 [=] Payment = 16.04166 — 45.00 = 28.95834— 45 [=] Balance = 3500.00 — 28.96 = 3471.04 2. 2275.25 X .05 = 113.7625 2275 025 05 113.7625 + 12 = 9.48020 12 [=] 9.48020 — 27.50 = 18.01980— 27 05 [=] 2275.25 — 18.02 = 2257.23 21 PROBABILITY PROBLEM: What is the probability of drawing the Ace, King, Queen, Jack, and Ten of Hearts in any order in five successive draws from a bridge deck. 5 4.38 2 1 ANALYSIS: P = — X = X= X 75 X ig __ 120 = ~ 811,875,200 2,598,960 Note: Move Decimal Point Selector to position 5X4 = 20 5 4 20 X 3 = 60 3 60 X 2 = 120 2 52 X 51 = 2652 52 51 2652 X 50 = 132,600 50 132,600 X 49 = 649,740 49 649,740 X 48 = 311,875,200 ‘ 48 311,875,200 + 120 = 2,598,960 [=] Conclusion: The probability of drawing the Ace, King, Queen, Jack, and Ten of Hearts in any order in five successive draws from a bridge deck is one chance in 2,598,960. 22 ACTUARIAL PROBLEM PROBLEM: Find the value at age 18 of a temporary life annuity of $1500.00 per year for three years. Assume an interest rate of 2%. FORMULA: a fal = 1Eis + 2Eis + 3Eis 953743* (.98039) + 951483 (.96117) + 949171 (.94232) 3] = (1500 a iss] = (1500) 955942 INDEX IN TOUCH CONTROL KEYS SOLUTION KEYBOARD IN SEQUENCE Note: Move Decimal Point Selector to position Store 1500 for use in step 6 below 1500 ENTER 9537438 X& .98039 = 935,040.09977 953743 ENTER 298039 + (951483 & .96117) = 1,849,577.01488 951483 ENTER 296117 + (949171 X .94232) = 2,743,999.83160 949171 ENTER 294232 Divide by Denominator = 2.87046 955942 [=] Multiply by $1500.00 = $4305.69 For an annuity of $1500 per period, the net single premium is $4305.69. *From “Commissioners 1941 Standard Ordinary Mortality Table.” 23 LIFE INSURANCE PROBABILITY PROBLEM: What is the probability that a person aged 35 will die in 10 years? FORMULA: The probability that a person aged x will die in n years is given by the formula: l, + n ndx = 1 —- —— ce | kk las 852554 54000 *e = _~—. _ = SOLUTION?®: 10435 = 1 ls 1 906554 ~ 906554 = .05957 (or roughly, the odds are 6 in 100) INDEX IN TOUCH CONTROL KEYS SOLUTION KEYBOARD IN SEQUENCE Note: Move Decimal Point Selector to position 852554 — ae = .05957 1 852554 906554 [=] [E] *NOTE: The table below is taken from the 1941 Commissioners Standard Ordinary Mortality Table and is the record of the number of deaths at different ages of a large number of persons. A Number Number of Yearly Probability ge Living Deaths of Dying x dy Qx 35 906,554 4,161 0.00459 45 852,554 7,340 0.00861 24 GEOMETRIC SERIES PROBLEM: Find the sum of 10 terms, beginning with the first, of the following geometric series: 15 16 etc 32 16 — arm 15 FORMULA: s = a ar a = Ist term = — 1-r 32 15 Yr = common ratio = 2 mo — x 210 32 32 Ss = 1-2 = 479.53 n = number of terms = 10 s = sum of the terms = ? INDEX IN TOUCH CONTROL KEYS SOLUTION KEYBOARD IN SEQUENCE Note: Move Decimal Point Selector to position 15 327 46875 15 ENTER 32 [+] [REPEAT 22 =4 2 [REPEAT] [x] [REPEAT] [STORE 24 = 16 REPEAT 28 = 256 REPEAT 210 = 1024 RECALL 2 x 210 = 46875 x 1024 = 480 32 15 15 — — (= x 210) = 47953125 — 39 (S x ) 53125 [=] Divide by Minus 1 = 479.53125 [CHANGE SIGN] [+] 25 STANDARD DEVIATION (Ungrouped Data) PROBLEM: X Values: 23 21 18 17 15 14 14 12 9 7 5 155 ux? maxX n Jo x 2499) — (155)? 7= 2499 155 11 n(2X?) — (2X)? n?2 TE = 5.35 SOLUTION INDEX IN KEYBOARD TOUCH CONTROL KEYS IN SEQUENCE 1. Enter 1st X value; square it. 2. Enter 2nd X value; square it. 3. Enter 3rd and subsequent X values. Repeat Step #2 (above) Read =X (155) in Register #1. 23 21 Note: Move Decimal Point Selector to position |[REPEAT| [REPEAT] [STORE |REPEAT| [REPEAT] [RECALL ] [+] [STORE | [+] * Touch |RECALL]. Now read 1X? (2499) in Register #1 and XX (155) in Register # 2. .niX2 = 27,489 . —(2X)? = 3,464 . Divide by n? = 28.62809 . Use the Square Root Application on page 38 to extract the square root of 28.62809. o = 5.35 RPO DN FH 11 155 11 *This operation causes <2 to be accumulated in the Memory Unit and =X to be accumulated in the Display. 26 VOLUME OF A SPHERE PROBLEM: Assume a sphere with a 7.26 inch radius. Find the volume. FORMULA: V = 4/37r? _ 4X 3.1416 x (7.26)? Vv 3 = 1602.87 cu. inches INDEX IN TOUCH CONTROL KEYS SOLUTION KEYBOARD IN SEQUENCE Note: Move Decimal Point Selector to position 4 ENTER 4X m = 12.56640 301416 (7.26)3 = 382.65717 7026 [REPEAT] [REPEAT] 4ar® = 4808.62306 Divide by 3 = 1602.87435 3 [=] 27 PROBLEM: Divide the angle 14° 22’ 6” into four equal angles. CONVERSION OF DENOMINATE NUMBERS 14° 22’ 6” \ \ NOTE: The same procedure used for degrees, minutes and seconds could be applied equally well to hours, minutes and seconds; yards, feet, inches; drams, ounces, pounds, etc. INDEX IN TOUCH CONTROL KEYS SOLUTION KEYBOARD IN SEQUENCE Note: Move Decimal Point Selector to position 1. Convert 14° 22’ 6” to Seconds (14° & 3600) = 50,400 14 ENTER 3600 + (22’ X 60) = 51,720 22 ENTER 60 Plus 6 seconds = 51,726 6 2. Divide by 4 = 12,931.5 4 [=] 3. Convert to Degrees, Minutes, Seconds (A) 12,931.5 + 3600 = 3.59208 3600 [=] 3 Degrees (B) (8.59208 —38) X 60 = 35.52480 3 [=] 35 Minutes 60 (C) (35.52480 — 35) X 60 = 31.488 35 [=] 31 Seconds 60 Therefore, the angle 14° 35’ 31” is divided into four equal angles of 3° 35’ 31” each. 28 AREA OF A SECTOR PROBLEM: Given the sector AXBS, find the area. Radius = AX = 94 feet Angle X = 50° 29’ 35” FORMULA: (457) am? = 50” 29" 35" 360 360 X 3.14159 x (94)? = 3893.44 Sq. Ft. Answer: 3893.4446748 = 3893.44 Sq. Ft. INDEX IN TOUCH CONTROL KEYS SOLUTION KEYBOARD IN SEQUENCE Note: Move Decimal Point Selector to position 1. Convert 50° 29’ 35” to a decimal equivalent 29 60 = .4833333 60 STORE 29 RECALL] [+] 29 35 _— —— = .4930. RECALL| |REPEAT 60 * 3600 30555 35 [RECALL] | 1x) [=] &) Plus 50° = 50.4930555 50 2. 50.4930555 + 360 = .1402584 360 [=] 3. Multiply by zr? 3.14159 X 94 X 94 3014159 94 REPEAT 29 INTERPOLATION PROBLEM: Find the Tangent of 27° 16’ 38” ANALYSIS: (1) Tangent 27° 16’ = .51540 (2) Tangent 27° 17’ = 51577 (3) The difference = 00037 (4) .00037 x 38 — 00023 60 (5) Tangent 27° 16’ 38” = .51540 + .00023 .51563 INDEX IN TOUCH CONTROL KEYS SOLUTION KEYBOARD IN SEQUENCE Note: Move Decimal Point Selector to position 1. Tangent 27° 16’ — Tangent 27° 17’ = .00037 051540 REPEAT 051577 [=] 2. 00037 X 38 _ poo93 38 60 60 [CHANGE SIGN] * Table of Natural Tangents and Cotangents 3. Tangent 27° 16’ 38” ll .51540 + .00023 .51563 24° 25° 26° 27° Tang Cotang Tang |Cotang | Tang Cotang Tang Cotang WONIAHATNPWNRO -44523 -44558 -44593 -44627 44662 -44697 -44732 44767 -44802 44837 -44872 -44907 -44942 44977 45012 -45047 -45082 45117 45152 -45187 -45222 2.24604 2.24428 2.23030 222857 2.22683 2.22510 2.22337 2.22164 2.21992 2.21819 2.21647 2.21475 2.21304 2.21132 -46631 | 2.14451 |.48773 -46666 | 2.14288 | .48809 -46702 | 2.14125 | .48845 -46737 | 2.13963 | .48881 -46772 | 2.13801 }.48917 -46808 | 2.13639 |.48953 -46843 | 2.13477 |.48989 -46879 | 2.13316 |.49026 -46914 | 2.13154 |.49062 -46950 | 2.12993 }.49098 -46985 | 2.12832 }.49134 -47021 | 2.12671 |.49170 -47056 | 2.12511 ].49206 -47092 | 2.12350 |.49242 -47128 | 2.12190 }.49278 -47163 | 2.12030 }|.49315 -47199 | 2.11871 |.49351 -47234 } 2.11711 |.49387 -47270 [2.11552 |.49423 -47305 |2.11392 }.49459 47341 [2.11233 |.49495 2.05030 2.04879 2.04728 2.04577 2.04426 2.04276 2.04125 2.038975 2.03825 2.03675 2.03526 2.03376 2.03227 2.03078 2.02929 2.02780 2.02631 2:02483 202335]. 2.02187]. 2.02039} . -50953 -50989 -51026 -51063 -51099 -51136 -51173 51209 -51246 -51283 51319 -51856 -51393 -51430 -51467 4|1.93746 1.96261 1.96120 1.95979) 1.95838) 1.95698 1.95557 1.95417 1.95277 1.95137 1.94997 1.94858) 1.94718) 1.94579) 1.94440) 1.94301 1.94162 1.94023 1.93885 1.93608 1.93470 4 *To eliminate the minus sign 30 EVALUATING AN INTEGRAL 5 PronLent: | 9x? — 4x2 + Bxdx = 1266.75 2 5 5 ANALYSIS: | 9x? dx —| 4x2 dx + 2 2 5 5 7 9 4 5 — 4 _ = 3 — y2 4* 3* | 1 2* 2 2 2 9 4 5 = (54 — 24) — = (53 — 93 2 (52 — 92 ra 24) 3 © 2) +56 2?) 1370.25 — 156 + 52.5 = 1266.75 INDEX IN TOUCH CONTROL KEYS SOLUTION KEYBOARD IN SEQUENCE Note: Move Decimal Point Selector to position 52 = 25 5 [REPEAT] |STORE]|RECALL] 5+ = 625 Q2 = 4 2 [REPEAT] 54 — 24 = 609 [REPEAT] [=] 609 X . = 1370.25 [=] 53 = 195 [RECALL] [REPEAT | 22 = 4 2 [REPEAT] [x] 53 — 23 = 117 2 [=] —(117 X 4/3) = 1214.25 4 3 Fl El 52 = 95 [RECALL] [REPEAT] 52 — 22 = 21 2 [REPEAT] [x] [=] [RECALL] 5 + (2 x 3) = 1266.75 2 [=] EVALUATING A POLYNOMIAL PROBLEM: Y = 4X# + 5X3 — 3X2?+ X —1 When X = 9 FIND: Y METHOD NO. 1 INDEX IN TOUCH CONTROL KEYS SOLUTION KEYBOARD IN SEQUENCE Note: Move Decimal Point Selector to position X2 = 92 = 81 9 [ STORE| |RECALL||REPEAT]| X4 = 94 = 6561 4X4 = 4 X 94 = 26,244 4 X3 = 93 = 729 | RECALL] [REPEAT] + 5X3 = + (5 X 93) = 29,889 5 X2 = 9? = 81 [RECALL] |REPEAT| — 8X? = — (3 X 9?) = 29,646 3 [=] + X = 29,655 — 1 = 29,654 1 [=] 382 EVALUATING A POLYNOMIAL PROBLEM: Y = 4X* + 5X% — 3X? + X -— 1 When X = —9 Find: Y METHOD: Y = {[(4X +5) X -3]KX4+1}X—-1 METHOD NO. 2 Note: Move Decimal Point Selector to position X= -9 9 [CHANGE SIGN|[STORE] 4X = —36 4 4X +5 = —81 5 (4X +5) X = 279 (4X +5) X — 3 = 276 3 [=] (4X +5) X — 3] K = —2484 (4X +5) X — 3] X +1 = —2483 1 {(4X +5) X — 3]X +1} X = 22347 {(4X +5)X—3]X+1}xX-1 1 [=] Y = 22,346 Now try this problem: Y = 25X3 — 14X? — 18X + 38. When X = 7, find Y. Answer (7801) 33 DETERMINANTS Solution of Simultaneous First Degree Equations PROBLEM: 2X + 2Y + 3Z = 22 2X — 4Y + 3Z 4 3X + 6Y — 2Z = 16 dy db, C1 ay d, C1 ds bs C2 ae d2 C2 dz b3 C3 as dz C3 > ¥ = a1 bi C1 ai bi Ci a2 bs C2 | a2 be C2 a3 bs c3 a3 bs c3 _ 176 + 96 + 72 + 192 — 396 + 16 | 16 +18 + 36+ 36 —- 364+ 8 | —16 + 198 + 96 — 36 —-96 +88 234 78 FORMULA: ayx + by + c12 = dy A2Xx + bey + Coz = dy asx + bsy + c3z = dz SOLUTION: + + + - N Numerator xX = Denominator 2 22 3 2 2 4 3 2 3 16 —2 3 Y = 2 2 3 2 2 —4 3 2 3 6 —-2 3 2 2 22 2 2 —A4 4 2 3 6 16 3 7, = 2 2 3 2 2 —4 3 2 3 6 —2 3 34 —128 + 24 + 264 + 264 — 48 — 64 © 78 78 312 78 3 4 Note: Move Decimal Point Selector to position DETERMINANTS PROCEDURE: I. II. TIT. TO FIND NUMERATOR . Index 22 [ENTER . Index 4 [CHANGE SIGN] . Index 2 [CHANGE SIGN] . Index 2 . Index 3 . Index 16 . Index 3 [ENTER . Index 4 . Index 6 . Index 16 . Index 4 [CHANGE SIGN] . Index 3 [=] . Index 6 . Index 3 . Index 22 [x] [F] . Index 2 [CHANGE SIGN] . Index 4 . Index 2 | © on oO Op won re e oO a rary e i) eee on we oo He jor) a 0 oon | TO FIND DENOMINATOR— FOLLOW SAME PROCEDURE AS IN I ABOVE TO FIND VALUE OF X 1. Touch [REPEAT] [STORE]. The denom- inator is now stored in the Memory Unit for subsequent use when solving for Y. The numerator now appears in Register #2; the denominator appears in Register #1. 2. Touch [=] . Value of X (2) appears in Register #1. IV. TO FIND VALUE OF Y 1. Calculate the top half of the second determinant. This produces the numerator (234). 2. Touch and [+]. This operation brings the denominator from the Memory Unit and divides it into the numerator. Then: 234 + 78 = 3. The value of Y (8) appears in Register #1. TO DETERMINE VALUE OF Z 1. The value of Z can be determined by calculating the third determinant as in IV above. 2. However, since value of X and Y are now known the value of Z can be easily de- termined by substituting values of X and Y in any of the three equations. For example: 2X + 2¥ + 3Z = 22 38Z = —2X — 2Y¥ + 22 —2X — 2Y + 22 a= 3 _ (2 X 2) — @ X 3) + 22 35 COSINE LAW PROBLEM: Given 8 sides find an angle. A a = 425.63 b = 339.29 c = 210.68 B a = 425.63 Cc REQUIRED: Cos C = .87213 Angle C = 29° 17’ 34” 2 2 _ 2 2 2 2 ANALYSIS: CosC = 2 +b cP (425.63)? + (339.29) (210.68) ~ ab 2 X 425.63 X 339.29 = 87218 INDEX IN TOUCH CONTROL KEYS SOLUTION KEYBOARD IN SEQUENCE Note: Move Decimal Point Selector to position TO FIND COSINE C (425.63)? = 181,160.8969 425 063 + (339.29)? = 296,278.601 339 029 — (210.68)? = 251,892.5386 210 68 [=] 2 X 425.63 = 851.26 2 425 «63 Cos C = ate = .87213 339 «29 [=] TO FIND ANGLE C (interpolate from Trig Tables: Cos 29° 17’ = .87221; Cos 29° 18’ = .87207) 87221 — 87207 = 14 87221 |STORE |[RECALL | 87207 [=] 87221 — 87213 = 8 87213 [=] 8/14 X 60” = 34.28571 60 Therefore: ZC = 29° 17’ 34” 14 [=] 36 COSINE LAW PROBLEM: Given two sides and the included angle, find the third side. FORMULA: c? = a? + b? — 2 ab Cos C EXAMPLE: a = 6.2 b = 83 56° 45’ 24” 4 C = 56° 45' 24” 8.3 Inches Cos C = .54819 6.2 Inches B INDEX IN TOUCH CONTROL KEYS SOLUTION KEYBOARD IN SEQUENCE Note: Move Decimal Point Selector to position ANALYSIS: c? = (6.2)? + (8.3)? — (2 X 6.2 X 8.3 X 54819) a2 = (6.2)2 = 38.44 602 REPEAT +b? = +(8.3)2 = 107.33 803 REPEAT 2a = 12.4 2 ENTER 602 2ab = 12.4-X 8.3 = 102.92 803 —2ab Cos C = 102.92 X .54819 054819 [=] a? + b? — 2ab Cos C = 50.91029 Using the square root application on page 38, ce = V50.91029 = 7.18514 = 7.185 37 SQUARE ROOT PROBLEM: Find the square root of 1738 to six significant digits. FORMULA: N at VN = 2 Where: N = the radicand (1738) a = an approximation of the square root of N ANALYSIS: Mark off 1738 into couplets. Start at the decimal point and mark off to the left; e.g. 17 38. Determine the largest square in the left most couplet. The largest square in 17 is 16. The The square root of 16 is 4. For each remaining couplet use a zero. The first approximation for V1788 is 40. EXAMPLES: 1) 98.22 The largest square is 81. The square root of 81 is 9 with no additional couplets to the left of the decimal. The approximation is 9. 2) 6 62 41.33 The largest square in 6 is 4. The square root of 4 is 2 with two additional couplets to the left of the decimal point. The approxima- tion is 200. 41.725 is the second approximation of the square root of 1738. DIVIDE, RECALL, PLUS, 2, DIVIDE. Third approximation = 41.68934 Fourth approximation = 41.68932 INDEX IN TOUCH CONTROL KEYS SOLUTION KEYBOARD IN SEQUENCE Note: Move Decimal Point Selector to position a 40 @ |STORE N 1738 @® |REPEAT] @ [RECALL] N — = 43.45000 ®@ [F] a N — + a = 83.45000 ® [RECALL [+] a : : a = 41.72500 2 2 [=] For closer values of V N, repeat the following sequence: STORE, REPEAT, RECALL, PROOF: Touch |REPEAT [x]. Answer: 1737.99940 or 1738 rounded off.