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

Jan 5, 2019

#1
+103131
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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

Jan 5, 2019
#2
+800
-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