I've undertaken an essay for my History class on the study of Babylonian mathematics. While studying I quickly came across the sexagesimal (base-60) number system. I'm getting a decent grasp on it but I'm (almost) completely lost when it comes to the reciprocals.
Here is an image of the reciprocal table I have come across:
If my understanding of base-60 is somewhat correct then the single number values are justified by setting the reciprocal over 60 and reducing, equalling the opposite of the number.
So for example for 2 = 30 I took 30/60 which reduced to 1/2 which makes sense to me because 1/2 is opposite of 2/1.
However, when it comes to the two digit terms such as 8 = 7,30 (which if i understand is 7 + 30/60 = 15/2 = 7.5) it doesn't make sense to me because it equals 7.5 and further down the list of two digit terms it gets more obscure.
Of course this system worked for them and is a legitimate number system but I can't seem to get a grasp on this. Any insight would be much appreciated.
For sexidecimal fractions we have
$$a,b =\dfrac{a}{60}+\dfrac{b}{60^2}$$
So
$$ 7,30 = \dfrac{7}{60}+\dfrac{30}{60^2}=\dfrac{1}{8} $$