Question

Which of the following represents the largest number?
A) 21 base eight
B) 18 base nine
C) 30 base four
D) 18 base eleven

Answer 1

What grade are you in?

Answer 2

I'm in a prerequisite math class in college. I haven't been in a math class for years.

Answer 3

Can you help me solve this?

Answer 4

Are these fractions?

Answer 5

No

Answer 6

Have you actually discussed base systems at all in class?

Answer 7

Not much. From what we have I don't understand it very well. But we start a new section on them this week.

Answer 8

Could you write 13 in binary?

Answer 9

So, I'll start with binary, then hopefully you'll be able to figure out how to do the question.

Answer 10

When I write out a number, say 56915, we are using what we call positional numbering- it matters not only what each digit in the number is, but also where it is. So, even though 56915 hase two '5's in it, actually each one represents a different number, one represents five and one represents fifty-thousand.

Answer 11

Oh okay so it is 18base11

Answer 12

Each time we move one position to the left, each digit is "worth" ten times more. So 56915 is actually \[5*10^4+6*10^3+9*10^2+1*10^1+5*10^0\]. It turns out that 10 is not really special at all for positional numbering, really it's just an evolutionary accident that we care about it at all. We could just as easily have used 2, and we might typically see numbers that look like 100110, which really just means \[1*2^5+0*2^4+0*2^3+1*2^2+1*2^1+0*2^0\], and which we would write "normally", or in base ten, as 38. in other terms, 100110b2=38b10.

Answer 13

Yes, it is.

Answer 14

So you're cool with this?