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To convert the base-7 number \(232055_7\) into a base-10 number, follow these steps:

We expand the base-7 number using powers of 7:

\[
232055_7 = 2 \times 7^5 + 3 \times 7^4 + 2 \times 7^3 + 0 \times 7^2 + 5 \times 7^1 + 5 \times 7^0
\]

Now, calculate each term:

\[
2 \times 7^5 = 2 \times 16807 = 33614
\]
\[
3 \times 7^4 = 3 \times 2401 = 7203
\]
\[
2 \times 7^3 = 2 \times 343 = 686
\]
\[
0 \times 7^2 = 0
\]
\[
5 \times 7^1 = 5 \times 7 = 35
\]
\[
5 \times 7^0 = 5 \times 1 = 5
\]

Now sum them all up:

\[
33614 + 7203 + 686 + 0 + 35 + 5 = 41543
\]

So, the base-10 equivalent of \(232055_7\) is **41543**.

Would you like more details or have any questions?

Here are 5 related questions for practice:
1. Convert \(123456_7\) to base-10.
2. Convert \(54321_7\) to base-10.
3. What is the base-7 representation of \(1000_{10}\)?
4. How do you convert a number from base-10 to base-7 manually?
5. How can you verify your base conversion result?

**Tip**: Always double-check each term in the expansion to avoid calculation errors during base conversions.

Convert the base-7 number 232055 to a base-10 number.

Learn how to convert the base-7 number 232055 into its base-10 equivalent with a detailed step-by-step solution. This example covers key mathematical concepts, including number systems and base conversion. Suitable for students in Grades 7-9.

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