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That is, eight asterisks and seven. That would be represented in base eight as 178. That is, one eight and seven ones. |
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You can represent the number fifteen in base ten as 1510, in base nine as 169, in base 8 as 178, in base 7 as 217. Why 217? In base 7 there is no numeral 8. In order to represent fifteen, you will need two sevens and one 1. |
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How do you generalize the process? To convert a base ten number to base 7, think about the columns: in base 7 they are ones, sevens, forty-nines, three-hundred forty-threes, and so on. Why these columns? They represent 70, 71, 72, 74, and so forth. Create a table for yourself: |
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The first row represents the column number. The second row represents the power of 7. The third row represents the decimal value of each number in that row. |
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To convert from a decimal value to base 7, here is the procedure: Examine the number and decide which column to use first. If the number is 200, for example, you know that column 4 (343) is 0, and you don't have to worry about it. |
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To find out how many 49s there are, divide 200 by 49. The answer is 4, so put 4 in column 3 and examine the remainder: 4. There are no 7s in 4, so put a zero in the sevens column. There are 4 ones in 4, so put a 4 in the 1s column. The answer is 4047. |
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To convert the number 968 to base 6: |
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There are no 1296s in 968, so column 5 has 0. Dividing 968 by 216 yields 4 with a remainder of 104. Column 4 is 4. Dividing 104 by 36 yields 2 with a remainder of 32. Column 3 is 2. Dividing 32 by 6 yields 5 with a remainder of 2. The answer therefore is 42526. |
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