Similarly, when if we wanted to convert 309 into base 6, we would start by making base 6 place values:īut we do not place the 309 into this table because 3 09 is not a base 6 number. We can do this by dividing: 123 ÷ 60 = 2, so we place 2 in the 60’s column and the remainder in the ones: We have to figure out how many 60’s and how many 1’s are in the number 123. Since 123 is not yet in Babylonian, we start with an empty base 60 table:Ĭonverting 123 into Babylonian is done by converting 123 into base 60. However, in example 2, to convert the number 123 to Babylonian, we did not multiply by the base 60 place values. We know we can place the base 5 number directly into the base 5 place values table because it is in base 5. Similarly, if we wanted to convert 243 5 into base ten, we would start by making base 5 place values, and then multiply by those values: When converting from Babylonian to base ten, we multiply by the base 60 place values. This is like converting 12 60 into base ten. In our first example, on page 2, we converted The Babylonians number systems can help us review how to convert between bases. With fewer people to keep track of, it is likely that the Babylonians were able to tell whether their neighbor had 61 “great cubits” of land or 3,601, or whether there were 61 goats next door or 3,601 goats, and so the lack of a zero may not have bothered them too much. However, think about how much smaller a society must have existed then – around 40,000 people lived in their largest city, as opposed to over 8,500,000 people in New York City today. This lack of a zero may seem as if it would have been a big problem. These same symbols could also be 3,660, if you imagine the space after the number. It would have been hard to tell if you had a space or not. Both have a 1, then another 1, but 3601 would have a space in between. Because of this lack of a zero, the symbols for 3,601 would have looked the same as the symbols for 61. There was one problem with the Babylonian number system – it did not have a symbol for zero. The Babylonians Did Not Have a Symbol for Zero Question: Convert the number 7812 into Babylonian. Tip: this is one number, in three separate place values, with | being the best the computer can do to show the Babylonian symbol for 1! Question: Convert the Babylonian number | ||| || into Hindu Arabic (our system). If we place 1 in the 3,600 place, we have 3,600 – 3,670 = 70 left, which is one 60, plus 10 left over: The next place value is 3600 because the place values were powers of 60, and 60 2 = 3600. Now we have a number large enough to need the next place value – the 3,600’s place. We start by dividing: 683 ÷ 60 = 11.38333…Since the system was base 60, the Babylonians could have up to the number 59 in any given place value, so putting 11 in one place value was just fine! Since 11 × 60 = 660, there was 683 – 660 = 23 left for the ones place.Įxample 4 Convert the number 3,670 to Babylonian. Answers to both questions are here.Įxample 3 Convert the number 683 to Babylonian. Question: Convert the number 187 into Babylonian. Question: Convert the number 67 into Babylonian. We know there are three left for the ones place because 2 × 60 = 120, and 123 – 120 = 3. To make the number 123 in Babylonian, since 123 ÷ 60 = 2.05, we know there are two 60’s. Since the system was base 60, this one was actually worth 60, similar to the way in which in the Hindu Arabic number 102, the 1 is actually worth 100.Įxample 2 Convert the number 123 to Babylonian. The space between the sets of symbols indicates that the first symbol for one is in a separate place value from the next two symbols. For example, 36 was made with 3 tens and 6 ones:īut the Babylonian system was actually a base 60, place value system, with place values of 60 0 = 1, 60 1 = 60, 60 2 = 3600, etc.Įxample 1 Convert the number below to our system (Hindu Arabic). At first glance, the system may seem additive, because they created the numbers from 1 to 59 by combining the ones and tens symbols.
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