Let's perform each of the operations with the given numbers \(3.25 \times 10^7\) and \(2.5 \times 10^5\):
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Addition: \(3.25 \times 10^7 + 2.5 \times 10^5\)
- To add these, we need to express \(2.5 \times 10^5\) in the same power of 10 as \(3.25 \times 10^7\): \[ 2.5 \times 10^5 = 0.025 \times 10^7 \]
- Now, adding: \[ 3.25 \times 10^7 + 0.025 \times 10^7 = (3.25 + 0.025) \times 10^7 = 3.275 \times 10^7 \]
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Division: \(3.25 \times 10^7 \div 2.5 \times 10^5\)
- Dividing: \[ \frac{3.25}{2.5} \times 10^{7-5} = 1.3 \times 10^2 \]
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Subtraction: \(3.25 \times 10^7 - 2.5 \times 10^5\)
- Using the same conversion as in addition: \[ 3.25 \times 10^7 - 0.025 \times 10^7 = (3.25 - 0.025) \times 10^7 = 3.225 \times 10^7 \]
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Multiplication: \(3.25 \times 10^7 \cdot 2.5 \times 10^5\)
- Multiplying: \[ 3.25 \cdot 2.5 \times 10^{7+5} = 8.125 \times 10^{12} \]
Now, matching the results to the given responses for the operations:
- \(3.25 \times 10^7 + 2.5 \times 10^5\) matches 3.275 * 10^7
- \(3.25 \times 10^7 \div 2.5 \times 10^5\) matches 1.3 * 10^2
- \(3.25 \times 10^7 - 2.5 \times 10^5\) matches 3.225 * 10^7
- \(3.25 \times 10^7 \cdot 2.5 \times 10^5\) matches 8.125 * 10^{12}
So the answers should be matched as follows:
- Addition: 3.275 * 10^7
- Division: 1.3 * 10^2
- Subtraction: 3.225 * 10^7
- Multiplication: 8.125 * 10^{12}