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The problem asks to convert the number \(43112_5\) (which is in base 5) to base 10.

We convert a base-5 number to base-10 by expanding it using powers of 5. Each digit is multiplied by 5 raised to the power of its position, starting from the right (which is position 0).

The number \(43112_5\) can be expressed as:
\[
4 \cdot 5^4 + 3 \cdot 5^3 + 1 \cdot 5^2 + 1 \cdot 5^1 + 2 \cdot 5^0
\]

Now let's calculate each term:
\[
4 \cdot 5^4 = 4 \cdot 625 = 2500
\]
\[
3 \cdot 5^3 = 3 \cdot 125 = 375
\]
\[
1 \cdot 5^2 = 1 \cdot 25 = 25
\]
\[
1 \cdot 5^1 = 1 \cdot 5 = 5
\]
\[
2 \cdot 5^0 = 2 \cdot 1 = 2
\]

Adding them up:
\[
2500 + 375 + 25 + 5 + 2 = 2907
\]

Thus, \(43112_5\) in base 10 is \(2907_{10}\).

Would you like a detailed explanation or have further questions?

Here are five related questions to deepen your understanding:
1. How would you convert a number from base 10 to base 5?
2. Can you convert the base-5 number \(1234_5\) to base 10?
3. How does the conversion change if the number is in base 2 instead of base 5?
4. What is the largest digit allowed in base 5, and why?
5. How do we perform addition and subtraction directly in base 5?

**Tip:** Always start the conversion from the rightmost digit when converting from any base to base 10.

Learn how to convert the number 43112 from base 5 to base 10. This detailed step-by-step solution explains the process of base conversion, including powers of 5 and multiplication. Ideal for students in Grades 7-9 studying number systems and base conversion.

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