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?

  • A 6.2 cm2
  • B 109 cm2
  • C 22 cm2
  • D 110 cm2
  • E 1.8 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?

  • A 40 cm2
  • B 60 cm2
  • C 10 cm2
  • D 50 cm2
  • E 80 cm2

Q4:

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

Measurement 1 2 3 4 5
Mass (g) 0.080 0.242 1.401 10.084 12.440

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?

  • A4
  • B1
  • C2
  • D3

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 1 2 3 4 5
Length (cm) 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 1 2 3 4 5
Length (cm) 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 0.2 cm, −0.2 cm
  • B 0.4 cm, −0.4 cm
  • C 0.3 cm, −0.3 cm
  • D 0.1 cm, −0.1 cm
  • E 0.5 cm, −0.5 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?

  • AGreater
  • BEqual
  • CLess

Q7:

Find the difference in the percent uncertainties of the two following measurements: 1 0 ± 0 . 5 s, and 5 ± 0 . 1 s.

  • A5%
  • B30%
  • C50%
  • D3%
  • E4.6%

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?

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