Subjects number theory

Base Five Conversion

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Base Five Conversion


1. The problem is to convert the number \texttt{31five} from base 5 to base 10. 2. The formula to convert a number from base $b$ to base 10 is: $$\text{Value} = \sum_{i=0}^{n-1} d_i \times b^i$$ where $d_i$ are the digits and $b$ is the base. 3. For the number \texttt{31five}, the digits are 3 and 1, and the base is 5. 4. Assign place values from right to left: the rightmost digit is $5^0$, the next is $5^1$. 5. Calculate each digit's contribution: $$3 \times 5^1 = 3 \times 5 = 15$$ $$1 \times 5^0 = 1 \times 1 = 1$$ 6. Add these values to get the base 10 number: $$15 + 1 = 16$$ 7. Therefore, \texttt{31five} in base 10 is $16$.