Q1. How many significant figures are in the following measurement: 0.0009?

A. 1
B. 5
C. 4
D. 3

Q2. Three unique samples are weighed on different scales at separate laboratories across the country. The first has a weight of 31.2 lbs, the second sample weighs 38.02 lbs, while the third measures 45 lbs. How much is the total combined weight of all of these samples?

A. 114.22 lbs
B. 110 lbs
C. 114 lbs
D. 114.2 lbs

Q3. A track coach measures the 100-meter time of a track athlete. The runner completes the distance in 11.5 seconds. If the stopwatch has an uncertainty of 1.7%, what is the amount of uncertainty in the time?

A. 11.5 s ± 0.19 s
B. 11.5 s plus or minus 0.19 s
C. 11.5 s ± 0.20 s
D. 11.5 s plus or minus 0.20 s
E. 11.5 s ± 0.1955 s
F. 11.5 s plus or minus 0.1955 s
G. 11.5 s ± 0.196 s

Q4. The speed of a bullet train is measured to be 312.0 mph ± 3.9 mph. What is the percent uncertainty in this measurement?

A. 1.3%
B. 1.2%
C. 1.25%
D. 0.0125%

The number 0.00091543 has 4 significant figures, the combined weight is 114.22 lbs, the time is less certain by approximately ± 0.20 s, and the bullet train's speed contains an uncertainty of about 1.25%.

Explanation:

Q1. The given measurement is 0.00091543. In this number, zeros leading the non-zero digits are not considered significant. So, this number has 4 significant figures.

Q2. To determine the combined weight, we simply add the three individual weights, 31.2 lbs + 38.02 lbs + 45 lbs. That gives a result of 114.22 lbs.

Q3. The uncertainty in time measurement can be found by multiplying the measurement with the percentage uncertainty. So, we have 11.5 s * 1.7/100 which equals 0.1955 s. So, the time is 11.5 seconds ± 0.1955 seconds, which we can round to 11.5 s ± 0.20 s keeping the same number of digits after the decimal place.

Q4. To calculate the percent uncertainty in the train's speed, we divide the uncertainty (3.9 mph) by the measured speed (312.0 mph) and multiply by 100. That gives us roughly 1.25%, which is the percent uncertainty in the speed of the bullet train.

Learn more about Significant Figures and Uncertainty here:

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