# Worksheet: Measurement Uncertainties

In this worksheet, we will practice converting between the absolute uncertainty and percent uncertainty in measured values.

**Q3: **

A marathon runner completes a course of 42.188 km in 2 h, 30 min, and 12 s. There is an uncertainty of 25 m in the distance traveled and an uncertainty of 1 s in the elapsed time.

Calculate the percent uncertainty in the distance.

- A0.059%
- B0.6%
- C0.59%
- D0.060%
- E0.06%

Calculate the percent uncertainty in the elapsed time.

- A1%
- B0.01%
- C0.1%
- D0.001%
- E0.011%

What is the average speed in meters per second?

What is the uncertainty in the average speed?

**Q7: **

A car speedometer has a uncertainty.

What is the range of possible speeds when the speedometer reads 85 km/h?

- A km/h
- B km/h
- C km/h
- D km/h
- E km/h

What is the possible range of speeds when the speedometer reads 85 km/h, stating this speed range in miles per hour, where 1 km = 0.6214 mi.

- A mph
- B mph
- C mph
- D mph
- E mph

**Q9: **

A set of seismographs record the arrival times of seismic waves from earthquakes, measuring these times to 0.100 s precision. To determine the distance to the epicenter of an earthquake, geologists compare the arrival times of S-waves and P-waves from the epicenter. If the S-waves and P-waves travel at 4.00 km/s and 7.20 km/s respectively, how precisely can the distance to the source of the earthquake be determined?

**Q10: **

Mass can be measured using a non-metric unit called the pound-mass. 1 lb=0.4539 kg.

If there is an uncertainty of 0.0001 kg in the pound-mass unit, what is its percent uncertainty?

- A2.0%
- B0.018%
- C0.024%
- D0.2%
- E0.02%

Suppose that there is a 0.1% uncertainty in the pound-mass unit. What mass in pounds would have an uncertainty in mass of 1 kg?

**Q11: **

The volume of gasoline dispensed at a commercial gas station for a nominal volume of 10 L was measured on five separate trials. The measured values were 9.89 L, 10.02 L, 10.30 L, 9.48 L, and 9.91 L. What is the mean volume and the standard deviation of the values?

- A and L
- B and L
- C and L
- D and L
- E and L

**Q12: **

The length of a pipe is measured with a meter stick. This measurement requires three uses of the stick since the pipe is more than 2 meters long. The first measured value is 1.00 m, the second measured value is also 1.00 m, and the third measured value is 0.76 m. The length of the pipe is the sum of the three measured values and each measured value has a measurement uncertainty cm. Find the length of the pipe and find the estimated uncertainty in the length by summing the fractional measurement uncertainties in quadrature.

- A m
- B m
- C m
- D m
- E m

**Q13: **

Two gauge pressures and are measured in order to determine the difference in pressure across an opening. Several measurements are made of each and it is found that mmHg and mmHg. What is the estimate of and the standard deviation of ?

- A mmHg and mmHg
- B mmHg and mmHg
- C mmHg and mmHg
- D mmHg and mmHg
- E mmHg and mmHg