Question
A 747 airplane weighs about 600,000 pounds. It can also be expressed as approximately 3 times 10 Superscript n tons. If there are 2,000 pounds in 1 ton, which is the most reasonable value of n?
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Answers
GPT-4o mini
To convert the weight of the 747 from pounds to tons and express it as approximately \(3 \times 10^n\):
1. First, we know that 1 ton is equal to 2,000 pounds.
2. Since the weight of the 747 is 600,000 pounds, we can convert this to tons:
\[
\text{Weight in tons} = \frac{\text{Weight in pounds}}{2000} = \frac{600,000}{2000} = 300.
\]
3. Now, we express 300 in scientific notation. \(300\) can be written as \(3 \times 10^2\).
4. Hence, we have:
\[
600,000 \text{ pounds} \approx 3 \times 10^2 \text{ tons}.
\]
From this, we can see that \(n\) is equal to \(2\). Therefore, the most reasonable value of \(n\) is
\[
\boxed{2}.
\]
1. First, we know that 1 ton is equal to 2,000 pounds.
2. Since the weight of the 747 is 600,000 pounds, we can convert this to tons:
\[
\text{Weight in tons} = \frac{\text{Weight in pounds}}{2000} = \frac{600,000}{2000} = 300.
\]
3. Now, we express 300 in scientific notation. \(300\) can be written as \(3 \times 10^2\).
4. Hence, we have:
\[
600,000 \text{ pounds} \approx 3 \times 10^2 \text{ tons}.
\]
From this, we can see that \(n\) is equal to \(2\). Therefore, the most reasonable value of \(n\) is
\[
\boxed{2}.
\]