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anonymous
 one year ago
Homework question: Mentally convert the base ten numeral 10 to a base five numeral. Image in comments.
anonymous
 one year ago
Homework question: Mentally convert the base ten numeral 10 to a base five numeral. Image in comments.

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mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Base 10 Base 5 0 0 1 1 2 2 3 3 4 4 5 10 6 11 7 12 8 13 9 14 10 ?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Here's another way of thinking of it. In base 10, there are 10 different digits. In base 5 there are five different digits. The number you want to write in base 5 happens to be twice the number of digits in base 5 numbers. What number is twice the number of digits in base 10 numbers?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0A way to think about it is through the basis representation theorem, which states that an integer n in base 10 can be expressed through the formula: n = a_0(k^s)+a_s(k^(s1))... where k represents the base that you are inputting into your head. a_0, a_1,... a_n are constants which are put together to form a number. An example makes this more clear. Like 10, lets say the number you want to represent is 5 in base 10 currently and convert it to base 5. number n is therefore 5 and base k is 5. 5 = a_0(5^0)+a_1(5^1) and the max number s you can exponentiate to is determined by how big your number is. a_1 = 1 and a_0 = 0, and the number is represented by (a_s)(a_s1)..., therefore it is 10. Try it out and solve the equation in your head for base 10 numbers in any other base.
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