Suppose the symbols to the right represents numerals in a base 4 numeratiion system .Write tha base 10 in Hindu-Arabic system

To convert a number from base 4 to base 10, we follow these steps:

1. **Identify the digits**: Each digit in the base 4 number has a place value that is a power of 4, starting from 0 on the right.

2. **Multiply each digit by its place value**: The place value is \(4^n\), where \(n\) is the position of the digit, counting from right to left starting with 0.

3. **Sum the results**: Add up all the products from the previous step to get the equivalent base 10 number.

### Example
Suppose the base 4 number is \( \text{213}_4 \).

1. **Identify the digits**: 2, 1, and 3.

2. **Assign place values**:
   - The rightmost digit (3) has a place value of \(4^0\).
   - The middle digit (1) has a place value of \(4^1\).
   - The leftmost digit (2) has a place value of \(4^2\).

3. **Calculate each term**:
   - \( 2 \times 4^2 = 2 \times 16 = 32 \)
   - \( 1 \times 4^1 = 1 \times 4 = 4 \)
   - \( 3 \times 4^0 = 3 \times 1 = 3 \)

4. **Sum the results**:
   - \( 32 + 4 + 3 = 39 \)

Thus, \( 213_4 \) in base 4 is equal to \( 39 \) in base 10.

If you provide the symbols or the exact base 4 number, I can perform the conversion for that specific number.

Would you like details or have any questions? 

### Related Questions:
1. How do you convert a base 10 number to base 4?
2. What is the general formula for converting any base \(n\) number to base 10?
3. Can you provide examples of conversions between different bases?
4. How does the place value system work in bases other than 10?
5. What are some common applications of base 4 numbering systems?

**Tip:** Always start converting from the rightmost digit when working with different bases.

Learn how to convert a base 4 number to base 10 using a step-by-step guide. Understand the place value system in different bases and practice with examples like converting 213 base 4 to base 10. Suitable for Grades 6-8 students and anyone interested in number systems and base conversions.

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