Generalised form of a three-digit number xyz is

Options

A. x + y + z
B. 100x + 10y + z
C. 100z + 10y + x
D. 100y + 10x + z

Answer

To find the generalized form of a three-digit number represented by the digits \( x \), \( y \), and \( z \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Place Values**:
- In a three-digit number, the first digit \( x \) represents the hundreds place.
- The second digit \( y \) represents the tens place.
- The third digit \( z \) represents the ones place.

2. **Assign Values Based on Place Values**:
- The value of the hundreds place (where \( x \) is located) is \( 100 \times x \).
- The value of the tens place (where \( y \) is located) is \( 10 \times y \).
- The value of the ones place (where \( z \) is located) is \( 1 \times z \).

3. **Combine the Values**:
- To express the three-digit number \( xyz \) in its generalized form, we add the values from each place:
\[ \text{Generalized form} = 100x + 10y + z \]

4. **Conclusion**:
- Therefore, the generalized form of a three-digit number \( xyz \) is \( 100x + 10y + z \).

### Final Answer:
The generalized form of a three-digit number \( xyz \) is \( 100x + 10y + z \).

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