If I cut something into 3 equal pieces, there are 3 defined pieces. But, 1÷3= .333333~. Why is the math a nonstop repeating decimal when existence allows 3 pieces? Is the assumption that it’s physically impossible to cut something into 3 perfectly even pieces?
In: Mathematics
Guy who dropped out of a math major bachelors degree program here lol- no, it’s not because of assumptions that it’s physically anything or whatever.
It’s because our number system is base 10. imagine your have a chocolate bar that is made up of 10 squares of chocolate and you have two others friends that you’re going to share the chocolate fairly with. How many chocolate squares do u give to each person?
Some cultures have used a base 12 or base 60 number system. A base 60 number system is kinda what we use to tell time with clocks. Let me show you what I mean using military time as an example. In military time 12:00 am is 00:00 and 01:00 am is 01:00 and 02:35 pm is 14:35. After 60 minutes go by, the number in the hours place goes up by one. So it’s kinda like the hours place number tells us how many groups of 60 minutes have gone by. Because 60 is a multiple of 3, a base 60 number system wouldn’t have that repeating decimal in the situation you described. Whats 1 hour divided by 3? Why it’s 20 minutes. 1hour/3= 20 minutes because 1 hour = 60 minutes. If I say the time is 13:10 then that means it have been (13*60 + 10) minutes since the day started.
What if we have a number system where none of the digits past 6 existed. So imagine 7,8, and 9 don’t exist and we counted in groups of 6 rather than groups of 10 like in our base 10 number system.
so our ways of counting and representing the numbers we counted is different.
5 (base 10) = 5 (base 6)
6 (base 10) = 10 (base 6)
7 (base 10) = 11 (base 6)
12 (base 10) = 20 (base 6)
35 (base 10) = 55 (base 6)
36 (base 10) = 60 (base 6)
0.5 (base 10) = 0.3 (base 6)
so in base 6 numbers, 10/3 = 2
and 1/3 = 0.2
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