To convert the number \(16\) from base \(9\) to base \(10\), we follow the process of evaluating the base \(9\) number using its positional values. 

### Step-by-Step Conversion

1. **Identify the digits and their positions:**
   The number \(16\) in base \(9\) has two digits: \(1\) and \(6\). In base \(9\), the rightmost digit represents \(9^0\), the next represents \(9^1\), and so on.

2. **Calculate the decimal (base 10) value:**
   \[
   16_{\text{base } 9} = 1 \times 9^1 + 6 \times 9^0
   \]
   Calculate each term:
   \[
   = 1 \times 9 + 6 \times 1
   \]
   \[
   = 9 + 6
   \]
   \[
   = 15
   \]

### Result

So, the number \(16\) in base \(9\) is equal to \(15\) in base \(10\).

Would you like more details or have any questions? Here are some related topics:

1. How to convert other base \(9\) numbers to base \(10\)?
2. How to convert base \(10\) numbers to base \(9\)?
3. Explanation of positional values in number systems.
4. How do base systems work for bases larger than \(10\) (like base \(16\) or base \(20\))?
5. Practical applications of base \(9\) or other non-decimal bases.

**Tip:** When converting from any base to decimal, multiply each digit by the base raised to the power of its position, starting from \(0\) on the right.

Learn how to convert the number 16 from base 9 to base 10 with this detailed step-by-step solution. Understand the concept of positional values and base systems, including the key formulas and methods for converting between bases. Suitable for students in Grades 5-7.

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