I'm struggling with understanding and using the Babylonian system to solve problems as well as the Mayan system, and I struggle most with converting from one base to the next.

For my course at the moment, with the Babylonian system I will only need to use numerals 1 and 10: Babylonian Numeral One and Babylonian Numeral Ten

An example of converting a Babylonian numeral to Hindu-Arabic numeral I need help with is Problem 1 and Problem 2

Next, I struggle with adding and converting Mayan numerals to expanded form. This is an example problem I struggle with: Problem 3

Finally, I would like to understand how you go from one base to another, particularly from base 10 to another base and from a particular base to base 10. Some examples come to mind; $$ 59_{ten} \to base\ two$$ $$ 40_{five} \to base\ ten$$ $$ 15_{eight} \to base\ twelve$$ $$ 40_{five} \to base\ ten$$ $$ 21_{six} \to base\ eight$$

I have a general idea how to do these things from my notes, but it seems like I can never apply the steps to homework and quizzes. For example, when I convert $299_{ten} \to base\ eight$, I take the place values $8^2, 8^1, 8^0$ and divide the evaluated form ($64, 8, 1$) starting with the numeral $299$. Then, I take the remainder from the first place value and divide it to the next place value, $8$. I repeat this process until I have a remainder of $0$, so then the answer is the grouping of all quotients from left to right; getting us $453_{eight}$. However, when I try this same process with $59_{ten} \to base\ two$ I end up with $111001_{two}$ when I should get $111011_{two}$ I have this issue with a lot of these problems. When I figure out how to solve one, solving another becomes alien. These are just high school problems I'm having, so if anyone could explain it simply that would be great.


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