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What is 59/15 in base 60? (Babylonian Division)

 Oct 27, 2016
 #1
avatar+26388 
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What is 59/15 in base 60? (Babylonian Division)

 

\(\begin{array}{rcll} \dfrac{59}{15} &=& 3 + \dfrac{14}{15} \\ 3 + \dfrac{14}{15} &=& 3\cdot 60^0 + \left[\dfrac{14}{15}\cdot 60\right]\cdot 60^{-1} \\ 3 + \dfrac{14}{15} &=& 3\cdot 60^0 + 56\cdot 60^{-1} \\ 3 + \dfrac{14}{15} &=& 3.56_{60}\\ \end{array}\)

 

laugh

 Oct 27, 2016
 #3
avatar+118658 
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What is 59/15 in base 60? (Babylonian Division)

 

 

 

\(59\div15\\ =59\times \frac{1}{15}\\ =59\times \frac{4}{60}\\ =59\times 0;4\\ = 0*59;4*59\\ =0;236\\ =236/60\\ =3;56\;\; babylonian\;\; number\\ =3.93\;base10 \)

 

or maybe I could have just said

 

\(\frac{59}{15}=3\frac{14}{15}\\ \frac{59}{15}=3\frac{56}{60}\\ \frac{59}{15}=3;56\;\;babylonian\;\; number\\ \)

 Oct 27, 2016

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