Something I found while reading about base systems, I can’t really wrap my head around it. Maybe it has to do with fractions?
In: 41
You have to read it as “base one zero”, not “base ten”.
Regardless of what number you pick as your base, in that base, it will always be written as “10”. In binary, you’d say “base two”, but in that binary code that nmumber two is written as “10”. Same for all other numbers.
That’s not coincidence, but basically the definition of a base. The number your number system is “based on” is defined as the first number for which you need a second digit, making the first digit a “1” (i.e. how often you counted to the base) and resetting the last digit to “0” (how much your remainder counts). In base 10, “10” simply means “one times ten plus zero times 1), in base 2 the same “10” means “one times two plus zero times one”.
A mindblowing example (for beginners) is hexadecimal (base 16). You write all numbers from 0 to 9 exactly as you know from base 10. Then you continue from 10 to 15 writing letters, i.e. A, B, C… until F. Finally, when you reach the sixteenth number, you exhaust the pool of available digits in base 16, so you need to add a new digit, so the number sixteen is written as “10” in hexadecimal (one times 16 plus zero). So in Hexadecimal, 9+7=10, but 10+7=17.
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