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Digital Measurements: Record all displayed digits and decimal places; Estimate the uncertainty using the largest of: o the manufacturer's specification, o the size of the fluctuations in the display, o the value of 1 in the last displayed decimal place (for example, a mass of 23.82 grams would have an uncertainty of ± 0.01 gram.) 1. A digital balance displays a mass of 0.1243 grams. In grams, what is the size of the uncertainty? ± 0.0001 g Analog Measurements: Estimate the first uncertain digit in the reading by estimating its distance between the smallest marked lines on the device. Mentally split the space between the marks into 2, 5, or 10 smaller divisions, convert this to a decimal, and record your answer using this as the final decimal place. The uncertainty in the reading is the size of your mental divisions. (Your instructor may require evidence for your answers to questions 2 - 4 below) 2. A ruler shows a measurement of length between 2.2 and 2.3 cm. The marks are closely spaced and you can imagine only one line between the two marked divisions. Record the length and the uncertainty in cm as a confidence interval, using ± format: (2.3-2.2)/2 = 0.1/2 = 0.05 cm (2.2+2.3)/2 = 4.5/2 = 2.25 ± 0.05 cm 3. A volume measurement is made in a cylinder with marks every 1 mL. You observe the volume is between 48 and 49 mL, and you estimate that it is about two-fifths of the way between the marks. Record the volume and the uncertainty in mL: 48 + 2/5 = 48.4 (49-48)/5 = 0.2 48.4 ± 0.2 mL 4. A volume measurement is made in a beaker with marks every 20 mL. The volume is between 20 and 40 mL and you estimate that it is about three-tenths of the way between the marks. Record the volume and the uncertainty and the units: (40-20)/10 = 2 20 + 3/10 = 20.3 20.3 ± 2 mL Calculated answers: Express the uncertainty to 1 significant figure, then round off the answer into the same decimal place as the uncertainty. Include units. 5. A calculation gave a density of 1.024666 g/mL and an uncertainty of 0.00333 g/mL. Re-express: 0.003 1.025 ± 0.003 g/mL Percent by mass solution: 6. You will prepare 40.0 grams of a NaCl solution that is 0.90 % by mass. Calculate the mass of NaCl that is needed (show work on the back of this page), and record it in your lab notebook.

Digital Measurements:
Record all displayed digits and decimal places;
Estimate the uncertainty using the largest of:
o the manufacturer's specification,
o the size of the fluctuations in the display,
o the value of 1 in the last displayed decimal place (for example, a mass of 23.82 grams would have an uncertainty of ± 0.01 gram.)
1. A digital balance displays a mass of 0.1243 grams. In grams, what is the size of the uncertainty?
± 0.0001 g
Analog Measurements:
Estimate the first uncertain digit in the reading by estimating its distance between the smallest marked lines on the device. Mentally split the space between the marks into 2, 5, or 10 smaller divisions, convert this to a decimal, and record your answer using this as the final decimal place.
The uncertainty in the reading is the size of your mental divisions.
(Your instructor may require evidence for your answers to questions 2 - 4 below)
2. A ruler shows a measurement of length between 2.2 and 2.3 cm. The marks are closely spaced and you can imagine only one line between the two marked divisions. Record the length and the uncertainty in cm as a confidence interval, using ± format:
(2.3-2.2)/2 = 0.1/2 = 0.05 cm (2.2+2.3)/2 = 4.5/2 = 2.25 ± 0.05 cm
3. A volume measurement is made in a cylinder with marks every 1 mL. You observe the volume is between 48 and 49 mL, and you estimate that it is about two-fifths of the way between the marks. Record the volume and the uncertainty in mL:
48 + 2/5 = 48.4 (49-48)/5 = 0.2 48.4 ± 0.2 mL
4. A volume measurement is made in a beaker with marks every 20 mL. The volume is between 20 and 40 mL and you estimate that it is about three-tenths of the way between the marks. Record the volume and the uncertainty and the units:
(40-20)/10 = 2 20 + 3/10 = 20.3 20.3 ± 2 mL
Calculated answers:
Express the uncertainty to 1 significant figure, then
round off the answer into the same decimal place as the uncertainty. Include units.
5. A calculation gave a density of 1.024666 g/mL and an uncertainty of 0.00333 g/mL. Re-express:
0.003 1.025 ± 0.003 g/mL
Percent by mass solution:
6. You will prepare 40.0 grams of a NaCl solution that is 0.90 % by mass. Calculate the mass of NaCl that is needed (show work on the back of this page), and record it in your lab notebook.

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