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Question 554447: Express 1845 to a numeral in base 13
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 1845 in base 10.
in base 13 it would be:
i believe the answer will be ABC
that would be:
C * 13^0 = 12 * 1 = 12 plus:
B * 13^1 = 11 * 13 = 143 plus:
A * 13^2 = 10 * 169 = 1690 equals:
1845
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the logic used is to divide the number in the base 10 by the base that you are wanting to convert to.
you would divide 1845 by 13 to get a quotient of 141 and a remainder of 12.
you would then divide 141 by 13 to get a quotient of 10 and a remainder of 11.
you would then divide 10 by 13 to get a quotient of 0 and a remainder of 10.
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your answer is in the order of the remainders from bottom to top.
your order is 10, 11, 12.
in the base of 13, 10 would be equal to A and 11 would be equal to B and 12 would be equal to C.
that makes your number in the base of 13 equal to ABC.
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the base 10 value of any base system is equal to the base 10 value of the least significant digit times the base raised to the 0 power plus the base 10 value of the next significant digit times the base raised to the 1 power plus the base 10 value of the next significant digit times the base raised to the 2 power, etc., until there are no more significant digits to process.
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the base 10 value of the number 1845 in the base of 10 is therefore equal to:
5 * 10^0 + 4 * 10^1 + 8 * 10^2 + 1 * 10^3 which becomes:
5 * 1 + 4 * 10 + 8 * 100 + 1 * 1000 which becomes:
5 + 40 + 800 + 1000 which becomes:
1845
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the base 10 value of the number ABC in the base of 13 is therefore equal to:
C * 13^0 + B * 13^1 + A * 13^2 which becomes:
C * 1 + B * 13 + A * 169 which becomes:
12 * 1 + 11 * 13 + 10 * 169 which becomes:
12 + 143 + 1690 which becomes:
1845
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in any base where the value of the digits in each position is greater than 9, alphabetic characters are used to represent the higher number.
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in the base 16 (hexadecimal system), therefore:
10 = A
11 = B
12 = C
13 = D
14 = E
15 = F
each position goes up to 15.
the number 17 in the hexadecimal system would be equal to:
17 divided by 16 equals a quotient of 1 with a remainder of 1.
quotient of 1 divided by 16 equals a quotient of 0 with a remainder of 1.
the hexadecimal equivalent number would be equal to 11.
the base 10 equivalent of tht number would be:
1 * 16^0 + 1 * 16^1 which would be equal to:
1 + 16 which would be equal to:
17.
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