|
Measurements are important in all sciences, but providing only a value and quantity is not enough. Every measurement should also specify its uncertainty. Uncertainty can be expressed using a plus/minus sign (±), but it can also be expressed by using an appropriate number of significant figures or decimal places. These uncertainties propagate through to the answer when, for example, adding or multiplying. Uncertainties arise in measurements from factors such as the measuring device, the skill of the operator, the environment, and the procedure. The effects of errors can be important, especially when a product requires tight tolerances. 
|
|
accuracy, precision, decimal places, significant figures
|
Review problems and questions |
|
- How many significant figures do the following numbers have?
203, 12.20, 0.05, −14.056, −0.0023, 100
|
203 has three significant figures.
12.10 has four significant figures.
0.05 has one significant figure.
−14.056 has five significant figures.
−0.0023 has two significant figures.
100 may have one, two, or three significant figures. Expressing this value in proper scientific notation will allow the number of significant figures to be clearly expressed. 
|
- You have five solid rods made of the same material. These rods all have the same cross-sectional shape (a 1 cm by 1 cm square) but are of different lengths. Below are some measurements you made of the length and mass of the rods.
Length x
(cm) | Mass m
(g) |
|---|
| 1.8 | 2.5 | | 2.2 | 3.4 | | 3.7 | 4.9 | | 4.2 | 5.9 | | 5.3 | 7.1 | - These measurements were taken using a ruler with gradations of 1 mm. Do these measurements match the precision of the instrument?
- As all of the rods are made from the same material, they should have the same density. Calculate the density for each of the five measurements. Are the densities the same to within the expected uncertainty? Based on the calculated densities, would you consider these measurements accurate?
- What could be some potential sources of uncertainty in the measurement of the length and mass of these rods?
- Your friend informs you that the ruler you used is missing the first two millimeters owing to wear and tear. This means that all of your measurements are 2 mm longer than they should be. Calculate the percentage error this causes in all five measurements of the length of the rods.
- How does the error caused by the shorter ruler change the error in the density calculation as the measured length becomes smaller?
|
- These measurements do match the precision of the instrument, as they all have a millimeter as the smallest amount measured.
- Densities: 1.4 g/cm3, 1.5 g/cm3, 1.3 g/cm3, 1.4 g/cm3, 1.3 g/cm3. These densities are similar; they indicate that the measurements are not accurate, however, as the densities are not equal to one another.
- Answers will vary but may include human error, a faulty ruler, a bad scale, and the temperature of the room affecting the length and density of the rods.
- The estimated errors in each length measurement are 11%, 9%, 5%, 5%, and 4%.
- The percentage error in the measured value increases as the length measured becomes smaller.
|
- A scientist has measured the weight of five objects of interest. Put these measurements in scientific notation: 450,000 g, 0.00089 g, 98.34 g, 2,340 g, and 0.0925 g.
|
450,000 g = 4.5×105 g
0.00089 g = 8.9×10−4 g
98.34 g = 9.834×101 g
2340 g = 2.34×103 g
0.0925 g = 9.25×10−2 g
|
- Your teacher hands you and your lab partner a box with a brand-new voltage source for conducting electricity experiments. What is the best way to figure out how to use the new equipment?
- Fiddle around with the equipment until you get it to work, because we learn best by doing.
- Let your partner unpack the equipment and fiddle with it while you search the Internet for information on what a voltage source is.
- Test the equipment for reliability by holding it under running water.
- Read the instruction manual and safety guidelines before trying to assemble or use the equipment.
|
|
d is correct.
|
Take a Quiz |
| |
|
