What is a Number Base?Date: 04/19/2003 at 13:37:55 From: Cathy Subject: Base Numbers The base eight number 7n3 is equal to the base 7 number 1n35. What digit does n stand for? I don't know what a base number is. Date: 04/19/2003 at 22:59:16 From: Doctor Samus Subject: Re: Base Numbers Hi Cathy, In order to understand this question, it is necessary to understand what it means for a number to be represented in a particular "base." Usually, we do math in the "base 10" system. What this means is that the right-most digit of a number represents the number of 1's (i.e. the number of 10^0's), the next digit over to the left represents the number of 10's (i.e. the number of 10^1's), and the nth digit over to the left from the right-most digit represents the number of 10^n's. For example, for the number 7068 in base 10, we know that the number represented is: 7 1000's (10^3's) + 0 100's (10^2's) + 6 10's (10^1's) + 8 1's (10^0's) = 7068 (in base 10). In general, a number represented in the "base x" system will have its right-most digit represent the number of 1's (since x^0 is always 1), and the nth digit over to the left from the right-most digit will represent the number of x^n's. For example, if x=4 (as in "base 4"), the number 3201 represents: 3 64's (4^3's) + 2 16's (4^2's) + 0 4's (4^1's) + 1 1's (4^0's) = 225 (in base 10). For your problem, we know you have 7n3 in base 8, so it represents the number: 7 64's (8^2's) + n 8's (8^1's) + 3 1's (8^0's) = 448 + 8n + 3 = 8n + 451 (in base 10). You also have the number 1n35 in base 7, so it represents the number: 1 343's (7^3's) + n 49's (7^2's) + 3 7's (7^1's) + 5 1's (7^0's) = 343 + 49n + 21 + 5 = 49n + 369 (in base 10). What would you do now to figure out the value of n? I hope this helps, but feel free to write back if you need further assistance. Thanks for writing in. - Doctor Samus, The Math Forum http://mathforum.org/dr.math/ |
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