To determine the fewest number of zeroes needed to write the value of each expression, we will simplify each expression to its standard form and count the zeros:
1. **\(7,820 \times 10^2\)**:
- \(7,820 \times 10^2 = 782,000\)
- Number of zeros: **3**
2. **\(36 \times 10^2\)**:
- \(36 \times 10^2 = 3,600\)
- Number of zeros: **2**
3. **\(459 \times 10^1\)**:
- \(459 \times 10^1 = 4,590\)
- Number of zeros: **1**
4. **\(15,000 \times 10^1\)**:
- \(15,000 \times 10^1 = 150,000\)
- Number of zeros: **5**
Now, we can put the expressions in order based on the fewest number of zeros, from least to greatest:
- \(459 \times 10^1\) - **1 zero**
- \(36 \times 10^2\) - **2 zeros**
- \(7,820 \times 10^2\) - **3 zeros**
- \(15,000 \times 10^1\) - **5 zeros**
### Final Order:
1. \(459 \times 10^1\)
2. \(36 \times 10^2\)
3. \(7,820 \times 10^2\)
4. \(15,000 \times 10^1\)