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The given number is in base-4, specifically "101313". To convert this base-4 number to base-10, we follow the procedure of expanding it using powers of 4.

The base-4 number "101313" is represented as:

\[
101313_4 = 1 \times 4^5 + 0 \times 4^4 + 1 \times 4^3 + 3 \times 4^2 + 1 \times 4^1 + 3 \times 4^0
\]

Now let's calculate each term:

\[
1 \times 4^5 = 1 \times 1024 = 1024
\]
\[
0 \times 4^4 = 0 \times 256 = 0
\]
\[
1 \times 4^3 = 1 \times 64 = 64
\]
\[
3 \times 4^2 = 3 \times 16 = 48
\]
\[
1 \times 4^1 = 1 \times 4 = 4
\]
\[
3 \times 4^0 = 3 \times 1 = 3
\]

Adding all these up:

\[
1024 + 0 + 64 + 48 + 4 + 3 = 1143
\]

Thus, the base-10 equivalent of the base-4 number "101313" is **1143**.

Would you like any more details or have any other questions? Here are some related questions to further explore the topic:

1. How do you convert other base numbers (like base-2 or base-8) to base-10?
2. What is the process of converting a base-10 number to base-4?
3. How would the base-4 number system be used in computing applications?
4. Why does the base-4 system use only the digits 0, 1, 2, and 3?
5. How can you quickly determine the place value in different bases?

**Tip:** When converting numbers from one base to another, breaking them down step by step and expanding them using powers of the base makes the process much easier.

Convert the base-4 number 101313 to base-10.

Learn how to convert the base-4 number 101313 to base-10 using step-by-step calculations. This problem covers number systems and base conversion concepts. Suitable for students in Grades 6-8.

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