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QuestionMathematics

What is the decimal representation of (10000)7
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Answer

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Step 1:
I'll solve this problem step by step using the specified LaTeX formatting guidelines:

Step 2:
: Understand the Problem

We need to convert the number (10000)₇ from base 7 to decimal (base 10) representation.

Step 3:
: Break Down the Base 7 Number

From right to left, the place values are $$7^{0}, 7^{1}, 7^{2}, 7^{3}, 7^{4}$$.
In base 7, each digit represents a power of 7.

Step 4:
: Expand the Number

10000_{7} = 1 \times 7^{4} + 0 \times 7^{3} + 0 \times 7^{2} + 0 \times 7^{1} + 0 \times 7^{0}

Step 5:
: Calculate Each Term

- $$0 \times 7^{0} = 0
- 0 \times 7^{3} = 0

Step 6:
: Sum the Terms

2401 + 0 + 0 + 0 + 0 = 2401

Final Answer

10000_{7} = 2401_{10}