So, how, using whatever methods you have, can you find Problem is mainly for you to become familiar with base 60. Their tables that they built up starting with 1, 2, 3. The following computation does the first product. ![]() The Babylonians would have found these reciprocals from Use our standard multiplication algorithm N which insures that its reciprocal is a finite sexagesimal 1,04 and 18 by 1,21 Divide 50 by 18 and 1,21 by 32 (using reciprocals). What is the condition on the integer Exercise 20 In the Babylonian system, multiply 25 by Tiplying 2, 3, and 5 only, then 1/n has a finite sexagesimalĮxercise 19. The analogous condition inīase 60 uses 2, 3, and 5. Only prime factors are 2 and 5 it is the case that 1/n hasĪ finite decimal representation. Now, what is the condition on n which insures that its re0 08,06, 0 04,10, and 0 05,33,20 to ordinary fractions in low- ciprocal is a finite sexagesimal fraction? The same questionĬan be asked about decimals in base ten, and you probablyįor the first one, note that 0 22,30 is 60 plus 602, and that already know the answer to that: for any number n whose Convert the sexagesimal fractions 0 22,30, Through a bit of computation is 0 39, 36.Įxercise 18. Since 7 times 12 is 60 plus 24, you’llįind that 7/5 = 1 24. To find 7/5 you would find the reciprocal of 5, which is 0 12,Īnd multiply that by 7. It’s your decision as to how close to the Babylonian ![]() Dividing the line 9 - 6:24 by 3 gives a line for The other reciprocals can be likewise found by dividingĢ and 3. One third of 20 is 6 23, that is 06,40.Įxercise 17. ![]() The reciprocal of 3 is 0 20, which without theĭecimal point is 20. Since 18 is twice 9,Īnd 9 is three times 3, the reciprocal of 18 can be found in Using this method you can find reciprocals of the other numbers.Īn easier way, and perhaps closer to the way the Babylonians did it, was to build up the table.
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