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Well Johanna, there are quick ways for some conversions, but not for others. Because I (like you I presume) work and think in base ten most of the time, I would first convert to base 10, then to the target base. For example, convert 40242 in base 5 to base 9. When we use different bases, we usually write a subscript after the number to indicate it isn't a base 10 number. e.g. 40242 in base 5 is written 40242_{5}. (a) convert to base 10 by repeatedly multiplying digits and sums by fives: (b) convert to base 9 by repeatedly dividing by 9 and recording the remainders: So 40242_{5} = 2572_{10} = 3467_{9}. There are faster ways for particular combinations of bases. For example, 4E20 in hexadecimal (base 16) is easily converted to base 2: 0100 1110 0010 0000. Because 16 is just 2^{4}, so each base 16 number turns into a four digit (with leading zeros) base 2 number. But this kind of trick doesn't work for just any two bases. Stephen La Rocque.  


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