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# What is 1/2 in base 3?

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What is 1/2 in base 3?

Guest Mar 22, 2018
#1
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1/2 base 10 = 0.11111111111111...in base 3

Guest Mar 22, 2018
#2
+94098
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$$\left(\frac{1}{2}\right)_{base 10}\\ = \frac{1}{3}+\frac{1}{6}\\ = \frac{1}{3}+\frac{1.5}{9}\\ = \frac{1}{3}+\frac{1}{9}+\frac{0.5*3}{27}\\ = \frac{1}{3}+\frac{1}{3^2}+\frac{1.5}{3^3}\\ = \frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+\frac{1.5}{3^4} \dots \\ =0.1111...._3\\ =0.\dot 1_{base 3}$$

there might be a better way of doing it, I am not sure about that.

Melody  Mar 22, 2018
#3
+92477
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That's very nice, Melody  !!!!

CPhill  Mar 22, 2018