Question

The speed of a bullet train is measured to be 312.0 mph ± 3.9 mph. What is the percent uncertainty in
this measurement to the correct number of significant figures?

1.3%
1.25%
1.2%
0.0125%

Answer 1

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:

1. Calculate the fraction:

\[
\frac{3.9}{312.0} \approx 0.01250
\]

2. 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%**