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What is the value of \(25_{10}+36_{10}\) in base 3?

 Jan 5, 2019
 #1
avatar+94209 
+1

2510 + 3610 =   6110

 

61 / 3  =  20(3)  R 1

20 / 3   = 6(3) R 2

6 / 3  =  2(3) R 0

2 / 3 =  0(3) R 2

 

Read the red numbers from bottom to top :

 

20213   =  2(3)^3 + 0(2)^2 + 2(3)^1 + 1(3)^0  =  54 + 6 + 1   =  61

 

 

cool cool cool

 Jan 5, 2019
 #2
avatar+534 
+1

\(25_{10}+36_{10}=61_{10}\)

Now, we see that \(3^3\) is the greatest power that fits in \(61\), and it fits twice.

\(61-3^3\times 2=7\)

Next, \(3^2\) doesn't fit, but \(3^1\) fits twice.

\(7-3^1 \times 2=1\)

Finally, \(3^0\) fits one time.

Therefore, the answer is \(2021_3\) because they fit twice, then never, then twice, then once.

 Jan 5, 2019

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