To calculate the percent uncertainty in the measurement of the bullet train's speed, we use the formula for percent uncertainty:
\[ \text{Percent Uncertainty} = \left( \frac{\text{Uncertainty}}{\text{Measured Value}} \right) \times 100% \]
In this case, the measured value is \(312.0 \text{ mph}\) and the uncertainty is \(3.9 \text{ mph}\).
Plugging in the values:
\[ \text{Percent Uncertainty} = \left( \frac{3.9}{312.0} \right) \times 100% \]
Calculating this step-by-step:
- Calculate the fraction:
\[ \frac{3.9}{312.0} \approx 0.01250 \]
- Convert to percent:
\[ 0.01250 \times 100% = 1.250% \]
Now, we round this result to the correct number of significant figures. The measurement with uncertainty (312.0 mph ± 3.9 mph) has 4 significant figures (312.0) and the uncertainty (3.9) has 2 significant figures. The result for percent uncertainty should reflect the least precise of these, which is 2 significant figures in this case.
Thus, rounding \(1.250%\) to 2 significant figures gives us:
\[ 1.3% \]
Therefore, the correct answer is:
1.3%
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