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2. The numerals in the upper left quadrant of the Babylonian hand tablet depicted on p. 67 are translated as: 5 tens combined with 3

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2. The numerals in the upper left quadrant of the Babylonian hand tablet depicted on p. 67 are translated as: 5 tens combined with 3 tens is 2 tens plus 5; that answer combined with 3 (ones) is 1 and 1 ten plus 5. (The answers are to the right of the vertical line.) For what operation(s) and place values is this computation correct? Explain. Then explain how a zero symbol would help to clarify this computation called a seragesimal system, just as ours is a decimal system. The num- bers 1 to 59 were represented by combinations of the two basic symbols used additively, with each V representing one and each representing ten. For instance, twenty-three was written as VVV The numbers from 60 to 3599 were repre- sented by two groups of symbols, the second group placed to the left of the first one and sep- arated from it by a space. The value of the whole thing was found by adding the values of the symbols within each group, then multiplying the value of the left group by 60 and adding that to the value of the right group. For instance, A hand tablet represented (10+1+1) .60 + (10+10+10+1) = 12.60+31=751. They wrote numbers 3600 (= 602) or greater by using more combi- nations of the two basic wedge shapes, placed further to the left, each separated from the others by spaces. Each single combination value was multiplied by an appropriate power of 60 - the combination on the far right by 60(-1), the second from the right by 601, the third from the right by 602, and so on. For example, 7883 was thought of as 2 3600 + 11.60+ 23 and written 2. The numerals in the upper left quadrant of the Babylonian hand tablet depicted on p. 67 are translated as: 5 tens combined with 3 tens is 2 tens plus 5; that answer combined with 3 (ones) is 1 and 1 ten plus 5. (The answers are to the right of the vertical line.) For what operation(s) and place values is this computation correct? Explain. Then explain how a zero symbol would help to clarify this computation called a seragesimal system, just as ours is a decimal system. The num- bers 1 to 59 were represented by combinations of the two basic symbols used additively, with each V representing one and each representing ten. For instance, twenty-three was written as VVV The numbers from 60 to 3599 were repre- sented by two groups of symbols, the second group placed to the left of the first one and sep- arated from it by a space. The value of the whole thing was found by adding the values of the symbols within each group, then multiplying the value of the left group by 60 and adding that to the value of the right group. For instance, A hand tablet represented (10+1+1) .60 + (10+10+10+1) = 12.60+31=751. They wrote numbers 3600 (= 602) or greater by using more combi- nations of the two basic wedge shapes, placed further to the left, each separated from the others by spaces. Each single combination value was multiplied by an appropriate power of 60 - the combination on the far right by 60(-1), the second from the right by 601, the third from the right by 602, and so on. For example, 7883 was thought of as 2 3600 + 11.60+ 23 and written

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