# Worksheet: Measurement Uncertainty and Resolution

In this worksheet, we will practice defining resolution-based and random measurement uncertainties and observing how they affect the values of measurements.

Q1:

The lengths of the sides of a sheet of paper are measured to be 7.8 cm and 14 cm. Rounding to an appropriate number of significant figures, what is the area of the sheet?

• A1.8 cm2
• B6.2 cm2
• C109 cm2
• D110 cm2
• E22 cm2

Q2:

A distance of 115 meters is measured to the nearest meter. The distance is run in a time of 12 seconds, measured to the nearest second. Rounding to an appropriate number of significant figures, what was the average running speed?

Q3:

The sides of a rectangular tile are measured to the nearest centimeter, and they are found to be 6 cm and 8 cm. Rounding to the same number of significant figures that the side lengths were measured to, what is the area of the tile?

• A40 cm2
• B50 cm2
• C60 cm2
• D10 cm2
• E80 cm2

Q4:

A 1-milligram resolution digital scale measures the masses shown in the table.

 Measurement Mass (g) 1 2 3 4 5 0.08 0.242 1.401 10.084 12.44

How many significant figures are in the first measurement?

How many significant figures are in the second measurement?

How many significant figures are in the third measurement?

• A3
• B1
• C4
• D2

How many significant figures are in the fourth measurement?

How many significant figures are in the fifth measurement?

Q5:

A 1 mm resolution measuring stick measures the lengths shown in the table.

 Measurement Length (cm) 1 2 3 4 5 0.2 0.9 1.2 2.1 10.2

How many significant figures are in the first measurement?

How many significant figures are in the third measurement?

How many significant figures are in the fifth measurement?

Q6:

The length of a metal pipe is measured, and the length varies slightly for different measurements. The measurements are shown in the table.

 Measurement Length (cm) 1 2 3 4 5 100.6 100.3 100.2 100.2 100.2

Find the mean length of the pipe.

Find the uncertainty in the length of the pipe due to its length changes.

• A cm
• B cm
• C cm
• D cm
• E cm

The pipe lengths are measured to a resolution of 0.1 cm. Is the uncertainty in the pipe length due to the precision of the measurements greater than, less than, or equal to the uncertainty due to the changes in the length?

• AEqual
• BLess
• CGreater

Q7:

Find the difference in the percent uncertainties of the two following measurements: s, and s.

• A
• B
• C
• D
• E

Q8:

A digital scale measures the mass of an object and the value it records is 0.50 kg.

What is the smallest mass the object could have that would be recorded as 0.50 kg instead of 0.49 kg? Give your answer to three decimal places.

What is the largest mass the object could have that would be recorded as 0.50 kg instead of 0.51 kg? Give your answer to three decimal places.

Q9:

A 20 cm long measuring stick has 50 evenly spaced lines marked along its length. What is the resolution of the measuring stick in millimeters?

Q10:

A 50 cm long measuring stick has 20 evenly spaced lines marked along its length. What is the resolution of the measuring stick in centimeters?

Q11:

A small object is measured using a measuring stick with marks 1 cm apart, as shown in the diagram. The left-hand end of the object is closer to the first mark (zero cm) than it is to the 1 cm mark, and the right-hand end of the object is closer to the 2 cm mark than it is to the 3 cm mark. What is the maximum length that the object could have?

What is the minimum length that the object could have?

What is the measured length of the object?

What is the uncertainty in the measured length of the object?

• A cm
• B cm
• C cm
• D cm
• E cm

Q12:

A small object is measured using a measuring stick with marks 1 mm apart, as shown in the diagram. The left-hand end of the object is closer to the first mark (zero length) than it is to the 1 mm mark, and the right-hand end of the object is closer to the 1 cm mark than it is to the 11 mm mark.

What is the measured length of the object in millimeters? What is the measured length of the object in centimeters?

What is the uncertainty in the measured length of the object, in centimeters?

• A0.01 cm, cm
• B0.03 cm, cm
• C0.04 cm, cm
• D0.05 cm, cm
• E0.02 cm, cm

Q13:

The diagram shows two digital timers that have different resolutions. Both timers display time in seconds. Which of the two digital timers has the higher resolution?

• A(b)
• B(a)

Which of the two digital timers can make more precise measurements?

• A(b)
• B(a)

Q14:

A measuring stick with marks one centimeter apart is used to measure two identical pencils, as shown in the diagram. The dashed lines show the point midway between adjacent centimeter marks. What is the length of one pencil, rounded to the nearest centimeter?

What is the total length of two pencils, rounded to the nearest centimeter?

Q15:

A small object is measured by two different measuring sticks, one that has marks 1 mm apart and another that has marks 1 cm apart, as shown in the diagram. The two measuring sticks are parallel to each other and their left-hand ends are at the same horizontal location. The left-hand end of the object is closer to the first mark (zero length) than it is to the 1 mm mark of the millimeter scale stick, and the right-hand end of the object is closer to the 1 cm mark than it is to the 11 mm mark of the millimeter scale stick. What is the measured length of the object in centimeters according to the centimeter scale stick?

What is the uncertainty in the measured length of the object using the centimeter scale stick?

• A
• B
• C0 cm
• D
• E

How many times smaller is the uncertainty in the measured length of the object as measured by the millimeter scale stick than the uncertainty in the length of the object as measured by the centimeter scale stick?

How many evenly spaced marks would need to be drawn between every two millimeter marks on the millimeter scale stick for it to be able to measure lengths with an uncertainty of ?

Q16:

The diagram shows two measuring sticks that have different resolutions. Which of the two measuring sticks has the higher resolution?

• AB
• BA

Which of the two measuring sticks can make more precise measurements?

• AB
• BA