~1~ Topic 1: Measurement Regents Chemistry Mr. Mancuso What is chemistry? The study of _________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________
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~1~
Topic 1: Measurement Regents Chemistry
Mr. Mancuso
What is chemistry?
The study of _________________________________________________________________
Descriptive units must follow all quantities (such as length, mass, and time)
Scientists use The International System of Units (SI units)
Base Quantity Name Symbol
Length
Mass
Time
Temperature
Amount of substance
Electric current
Light intensity
*Volume
* Heat
* NOT SI units, but used often in chemistry.
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Reference Table B SI units are based on the power of 10, and are written in decimals – not fractions.
Prefix Symbol Value
mega ‐
kilo ‐
deca ‐
*Base units
deci‐
centi‐
milli‐
micro‐
nano‐
~4~
Converting Measurements
Dimensional Analysis / “Factor‐Label Method”
Cross‐out equal units through the problem until you get the unit desired
Let’s say we wanted to convert the following: (1) 320 grams into kilograms
(2) 12 weeks into hours
~5~
“Moving the decimal” Method
K H D B D C M Base unit
King Hector Died By Drinking Chocolate Milk
(kilo‐) (hecto‐) (deca‐) BASE (deci‐) (centi‐) (milli‐)
420 g = __________ mg
Identify placement of each value
k h d b d c m
Move the decimal to match
1 2 3
k h d b d c m
4 2 0 0 0 0
420,000 mg
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Guided Practice Name each unit and identify what it measures
1. km _______________________________ _________________________ 2. mg _______________________________ _________________________
Perform the following conversions 1. 1 cm = _______________ m 2. 2 kg = _______________ g 3. 400 mL = ________________ L 4. 200 mm = ________________ m
5. 0.0025 m = _______________ m 6. How many kilograms are there in 125 g of a substance? 7. Find the number of centimeters in 5 kilometers.
8. Convert 1.0023 m into cm. 9. How many L are in 623.5 mL?
~7~
10. Convert 36 days into milliseconds. 11. Convert 8 x 107 micrometers into inches (1 inch = 2.54 cm).
Student Practice Name each unit and identify what it measures
1. g _______________________________ _________________________ 2. cm _______________________________ _________________________ 3. mL _______________________________ _________________________ Perform the following conversions: 4. 1 kg = _______________ g 5. 9 L = ________________ mL 6. 6 g = ________________ cg 7. 250 mg = ________________ kg 8. 12.1 mm = _______________ cm 9 1.5 Ms = _______________ s
~8~
10. Find the number of milligrams in 0.5 kilograms. 11. Convert 5 meters to kilometers. 12. Find the number of ms in 5.268 s. 13. Convert 1200.0035 dag into cg. 14. How many mm are in 35.002 dm? 15. Convert 28.5 kilometers into yards (1 m = 1.093 yard) 16. Convert 3.2 x 10‐3 Joules into calories (1 J = 0.2390 calorie)
~9~
Significant Figures Data collection is limited by the technology of the measuring device.
a. Precision: ______________________________________________________________
b. Accuracy: ______________________________________________________________
Let’s say that you mass 1.00 mL of pure water (known density 1.00 g/mL)
Scale #1 Scale #2 Scale #3
Meas. #1
1.32 g
4.20 g
1.01 g
Meas. #2
-2.30 g
4.18 g
0.99 g
Meas. #3
18.09 g
4.18 g
0.98 g
Precision
Accuracy
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Significant Figures:
o The digits in a measurement having values that are known with certainty. PLUS one digit with an estimated value If there is no decimal present, begin counting from right to left, starting at the first
non-zero
If there is a decimal, begin counting from left to right, starting at the first non-zero
o “USA rule”
o For numbers in scientific notation, all numbers before (________ x 10x) are significant.
o The technology of the equipment that a scientist uses will limit the number of significant figures.
~11~
Guided Practice 1. 0.02 ________________
2. 0.020 _______________
3. 501 _________________
4. 501.0 _______________
5. 5,000 _______________
6. 5,000. _______________
7. 6,051.00 _____________
8. 0.0005 ______________
9. 10,001 ______________
10. 0.1020 ______________
11. 0.0010 ______________
12. 10020 ______________
13. 1.00 x 1023 ___________
14. 4.0 x 103 _____________
15. 30.300 ______________
Student Practice 16. 8040 _______________
17. 0.0300 ______________
18. 699.5 _______________
19. 2.000 x 102 ___________
20. 0.90100 _____________
21. 90,100 ______________
22. 4.7 x 10‐8 ____________
23. 10,800,000. __________
24. 3.01 x 1021 ___________
25. 0.000410 ____________
26. 12.00 _______________
27. 0.00230 _____________
30. 129 ________________
31. 5,007 ______________
32. 100.0 _______________
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ACTIVITY: POGIL – Significant Measurement
Student Practice Measuring with thermometers (°C) Everything that is known, and one estimated digit.
Measuring volume with graduated cylinders (mL) Everything that is known, and one estimated digit.
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Scientific Notation
Always written as: ________ x 10x
Values of one and higher have a ___________________ superscript
Values lower than one have a ____________________ superscript
All digits found before (x 10x) must be included in standard notation conversion
Guided Practice Convert the following to scientific notation.
1. 0.005 = _________________________
2. 0.25 = ___________________________
3. 5,050 = ________________________
4. 0.025 = __________________________
5. 0.0008 = _______________________
6. 0.0025 = _________________________
7. 1,000 = ________________________
8. 500 = ____________________________
9. 1,000,000 = _____________________
10. 5,000 = __________________________
Convert the following to standard notation.
1. 1.5 x 103 = ______________________
2. 3.35 x 10‐1 = _______________________
3. 1.50 x 10‐3 = ______________________
4. 1.2 x 10‐4 = ________________________
5. 3.75 x 10‐2 = _____________________
6. 1 x 104 = _________________________
7. 3.75 x 102 = ______________________
8. 1.002 x 10‐1 = ______________________
9. 2.2 x 105 = _______________________
10. 4 x 101 = _________________________
~14~
Student Practice Identify the number of significant digits and convert the following to scientific notation.
1. 783.4 = ________________________
2. 0.32800 = _________________________
3. 1000.0 = ________________________
4. 102300 = _________________________
5. 0.2000 = ________________________
6. 4200.00 = ________________________
7. 4300 = _________________________
8. 0.0000800 = _____________________
Convert the following to standard notation.
1. 2.003 x 10‐3 = _____________________
2. 9.803 x 10‐2 = _____________________
3. 7.100 x 103 = _____________________
4. 6.02 x 108 = _______________________
5. 9.01230 x 10‐4 = ___________________
6. 8.00 x 10‐3 = ______________________
7. 1.23 x 104 = ______________________
8. 2.10 x 10‐2 = ______________________
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Calculations Involving Significant Figures
Rules for Multiplying and Dividing
Identify the number of significant digits in each value of the problem
Do the calculation
Your answer may only contain equal amounts of significant digits as the value in the problem with the least. Rounding may be necessary.
Use scientific notation when necessary
Include proper unit in the answer: May be a derived unit! (ex: m2, m3, m/s, or no unit)
As a general rule, if the question is in scientific notation, the answer should be also
Rules for Adding and Subtracting
Do the calculation
Answer may only contain equal amounts of decimal points as the value with the least number of decimal points in the question
Round when necessary. Include the unit (stay the same).
In order to add or subtract numbers, they must be in the same unit. Converting may be
necessary.
For Problems with Multiple Functions
Calculate through the entire problem without using significant figures
Take your final calculated number and apply the rules for significant figures o If multiplication or division was used, base your answer on those rules,
otherwise apply the rules for addition and subtraction
~16~
Guided Practice Perform the following operations, and express your answer in the correct number of significant figures. Show all work.
1. 1.35 m x 2.467 m ___________ 2. 1,035 m2 ÷ 42 m ___________ 3. 12.01 mL + 35.2 mL + 6 mL ___________ 4. 350.0 J + 0.05 kJ (solve for Joules) ___________
5. 52.8 Pa + 3.0025 Pa 252.5 Pa ___________
6. 7 x 10‐3 x 1.2 x 109 ___________
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7. 8.75 x 104 + 2.513 x 105 ___________ 8. 1.6305 g ÷ 2.0 m3 ___________
9. 3.20 g + 0.03 g ___________
10. (56.6 s + 30.0 s + 0.10 s) x (78.86 s ‐ 19.2 s) ___________ 11. 1.278 x 103 m2 ÷ 1.4267 x 102 m ___________
12. 55.46 g ‐ 28.9 g ___________
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Student Practice Perform the following operations, and express your answer in the correct number of significant figures. Show all work.
SET A 1. 0.21 cm x 3.2 cm x 100.1 cm ___________ 2. 0.15 cm + 1.15 cm + 2.051 cm ___________ 3. 150 L3 ÷ 4 L ___________ 4. 603.2 kJ x 5.8 J (solve for Joules) ___________ 5. 27.8 m ‐ 529.4 cm (solve for meters) ___________ 6. 505 kg ‐ 450.25 kg ___________ 7. 1.252 mm x 0.115 mm x 0.012 mm ___________ 8. 0.3287 g x 45.2 g ___________
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9. 125.5 kg + 52.68 kg + 2.1 kg ___________ 10. (0.12 g + 5.16 g) x (45.56 g ‐ 93.0 g) ___________ 11. 68.32 ns + (‐1.001 ns) + (‐0.00367 ns) + (‐678.1 ns) ___________ 12. 0.258 mL ÷ 0.36105 mL ___________ 13. 27.01 kg + 1532.8 g (solve for kg) ___________ 14. 1250 J ‐ (234.207 J2 ÷ 52.69 J) ___________ 15. 78.26 L ‐ 89.50 L 678.2 L + 9511 L ___________ 16. 100 s ‐ 1.3 s ___________ 17. 19.32 mm + 0.0022 m (solve for mm) ___________ 18. 100. cm ‐ 1.6 cm ___________
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SET B 19. 4302 g + 0.8037 g ___________ 20. 5.7 cm x 0.20 cm ___________ 21. 10.2 s ÷ 0.4 s ___________ 22. 3.6 x 102 ÷ 4.8 x 108 ___________ 23. 3.6 x 10‐8 ‐ 4.5 x 10‐7 ___________ 24. 7.2 x 10‐2 x 5.1 x 10‐3 ___________ 25. 6.15 m x 3.026 m x 0.018 m ___________ 26. 6.003 cm + 4.8 cm + 7 cm ___________ 27. 3 cm x 43 cm ___________
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28. 75.3 g ÷ 3.0 mm ___________ 29. 5.00 x 103 mL x 25 mL ___________ 30. 8.03 x 10‐3 m2 ÷ 0.037 m ___________ 31. 0.0023 g x 12 ___________ 32. 0.09 L ÷ 2.4 s ___________ 33. 100 s + 100.0 s ___________ 34. 12.30 J + 12.326 J ___________ 35. 2 m x 6.3 ___________ 36. 999 m ÷ 4 s ___________
~22~
Density
The distribution of mass per unit of volume
Used to identify substances, since a substances density is always constant:
i. Water = 1.00 g/mL ii. Gold = 19.3 g/mL iii. Iron = 7.90 g/mL
Formula:
o Pepsi vs. Diet Pepsi
~23~
Guided Practice Solve each of the problems below, and express your answer in the correct number of significant figures. Show all work
1. An object has a mass of 57.7 g and occupies a volume of 21.65 cm3. Calculate its density.
2. A sample of a substance whose density is 4.19 g/cm3 occupies 0.11 cm3. What is the mass of this sample?
3. Calculate the mass, in kilograms, of an object that occupies 25.3 cm3 and has a density of 4.14 g/cm3?
4. A sample of a powdered solid has a mass of 9.88 g and occupies 8.623 cm3. A sample of another powdered solid has a volume of 31.62 cm3 and a mass of 32.74 g. Calculate the overall density of a mixture on these two samples.
~24~
Student Practice Solve each of the problems below, and express your answer in the correct number of significant figures. Show all work
1. What is the volume of a 29.6 g sample of a metal that is known to have a density of 5.15 g/cm3? 2. If the density of silver is 10.5 g/cm3, what is the mass of a sample of silver that occupies 965 cm3? 3. A certain gas under given conditions has a density of 1.34 x 10‐4 g/cm3. What volume will 250.0 g of this gas occupy under the same conditions?
~25~
4. An object is found to have a mass of 1.9340 kg and occupies a volume of 542 cm3. Calculate its density in g/cm3. 5. Two liquids are mixed together. The mass and the volume of the first liquid are 72.7 g and 68.7 cm3, respectively. The mass and volume of the second liquid are 44.3 g and 57.5 cm3, respectively. Calculate the total mass and volume of the mixture and calculate its overall density. 6. Iron has a density of 7.86 g/cm3. Could a block of metal with a mass of 18.2 g and a volume of 2.56 cm3 be iron? Explain.
~26~
Pre-Quiz Review At 25°C, 10.0181 g of an unknown liquid was found to have a volume of 6.75 mL.
1. Calculate the density of the liquid.
2. Which of the following liquids was the unknown?
Density, g/mL at 25°C
Water 0.9982
Toluene 0.8669
Chloroform 1.4832
3. If the unknown liquid has been water, what would the volume have been?
4. What mass would a 10.00 mL sample of each of the liquids in (2) have?
Water _________________
Toluene _________________
Chloroform _________________
~27~
5. A stopper was found to have a mass of 5.06 g. When placed in a graduated cylinder
containing 45.2 mL of water, the volume of the stopper and water was found to be 49.4 mL. Calculate the density of the stopper.
6. A chemist was given four unidentified, water soluble cubes measuring 1 cm x 1 cm x 1 cm and asked to arrange these substances in order of their increasing density. These cubes were labeled A, B, C, and D. As a reference, the chemist was also given the following liquids, whose densities in g/mL at 20°C are given below:
Water 0.9982
Toluene 0.8669
Nitromethane 1.1371
Chloroform 1.4832
The chemist added one of the four substances to one of the liquids and observed whether the substance floated or sank. By repeating this procedure with the other substances and liquids, he was able to make a series of observations about the relative densities of the substances and the liquids. Use the following selected observations to arrange the four unknown substances in order of increasing density. Briefly defend your order. (i) Substance A sank in chloroform (ii) Substance B floated in water but sank in toluene (iii) Substance C sank in water but floated in chloroform and nitromethane (iv) Substance D sank in nitromethane but did not sink as rapidly as Substance A did in
nitromethane _____________ _____________ _____________ ____________ Least dense Most dense
~28~
Percent Error
Percentage error is a way for scientists to express how far off a laboratory value is from the commonly accepted value.
The significant figures in the final answer is based on the measured and accepted values. The “x 100” is not considered.
The formula is:
100 x valueaccepted
valueaccepted - valuemeasured error %
Guided Practice Determine the percentage error in the following problems. Show your work. Use significant figures.
Experimental value = 1.24 g Accepted value = 1.30 g Answer_____________ Experimental value = 1.24 x 10‐2 g Accepted value = 9.98 x 10‐3 g Answer_____________ Experimental value = 252 mL Accepted value = 225 mL Answer_____________
~29~
Student Practice Determine the percentage error in the following problems. Show your work. Use significant figures.
1. Danielle measures the width of a room & gets a value of 26 ft. A contractor measures it & determines it to actually be 26.25 ft. What is the percent error of Danielle's measurement?
2. A laboratory student was asked to measure the volume of an unknown liquid. After pouring the
liquid into a graduated cylinder, the student incorrectly read the volume as 34.6 mL. If the correct volume of the liquid was 32.6 mL, what was the percentage error?
3. A metal block has a density of 3.245 g/cm3. If a student determined the density to be 2.5 g/cm3,
then to what percent was his measurement incorrect? 4. An 8‐year old girl guessed that the sun was 100 miles away from the Earth. The sun is actually
9.3 x 107 miles away. What was this girl’s percent error?
~30~
The Scientific Method The way scientists solve problems.
X‐axis is always horizontal and the independent variable
Y‐axis is always vertical and the dependent variable
Label X and Y axis o NOT as “X” and “Y” o Be specific and concise o Use appropriate units
Both axis’s arranged to their own scale o Preferably start at zero, but may start at any logical number o Difference between first and second number determines the scale o Do not use “breakers”
When plotting data, plot only those values that are given. o Do not plot for zero unless a value is given for zero
Circle all points
The three typed of graphs that you will be required to draw:
o “Connect the points” Line Graph
o Best‐Fit Curve Curved line through the general trend of the data, without going through all
the points
o Best‐Fit Line Straight line that shows the slope of the graph, without going through all the
points
Give the graph a relevant title o Title must be describe the reason for the graph o “Independent vs. Dependent”
~33~
Skills Development: Best Fit Line Follow all directions below:
Label and scale the X‐axis and Y‐axis, including appropriate units Plot the data on the table, and circle the points. Draw a best fit line. Give the graph a title Predict how many accidents there would be when there are 70,000 cars on the road
# of cars on the road # of accidents
100,000 75
93,000 66
83,000 57
78,000 53
63,000 41
52,000 30
40,000 23
33,000 17
27,000 15
13,000 8
7,000 5
~34~
Skills Development: Best Fit Curve Follow all directions below:
Year Population of Buffalo (x 103)
1908 243
1912 247
1920 259
1924 283
1928 320
1932 316
1936 340
1948 403
1952 632
1956 646
1960 632
1964 795
1968 925
1972 1,013
1976 1,243
Label and scale the X‐axis and Y‐axis, including appropriate units Plot the data on the table, and circle the points. Draw a best fit curve. Give the graph a title Predict the time for the population of Buffalo in the year 1980
~35~
Lab Equipment *Study and know for all tests and quizzes
Unit One Review
____ 1. Chemistry is best defined as the study of: (1) matter (2) all substances and the changes that they can undergo (3) the substances found on the periodic table and the compounds they form (4) what happens when two elements are mixed together
____ 2. Chemistry has been called the central science because it:
(1) is the most important (2) was the first science developed (3) in intermediate in usefulness (4) overlaps many sciences
____ 3. A tentative or suggested answer to a question, formulated before experimentation, is called a(n): (1) natural law (3) hypothesis (2) observation (4) theory ____ 4. The factor being tested in an experiment is called the: (1) hypothesis (3) natural law (2) observation (4) variable ____ 5. An idea that describes how nature behaves but does not explain why nature behaves in the way it does is called a(n): (1) hypothesis (3) natural law (2) observation (4) theory ____ 6. In science, a properly formulated hypothesis:
(1) must always be able to be tested (2) can either be tested or accepted on logic (3) cannot be tested (4) is proposed only after testing is completed
____ 7. An experimental control:
(1) is a factor being tested or changed (2) keeps all conditions constant during an experiment (3) responds in a predictable way to the experiment (4) is a device used to measure the accuracy of an instrument
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____ 8. What is the SI unit for mass? (1) kilogram (3) liter (2) mole (4) gram ____ 9. Which of the following is a derived unit? (1) kilogram (3) mole (2) cubic centimeters (4) Kelvin ____ 10. What is the abbreviation for millimeter? (1) mM (3) mm (2) Mm (4) μm ____ 11. The liter is a non‐SI unit of: (1) length (3) mass (2) area (4) volume ____ 12. Which of the following is an instrument used to measure liquid volume? (1) balance (3) thermometer (2) evaporating dish (4) graduated cylinder ____ 13. A recorded measurement has two certain digits and one estimated digit. How many significant digits does the measurement have? (1) none (3) two (2) one (4) three
____ 14. In which of the following is the zero not significant? (1) 0.15 (3) 1.50 (2) 1.05 (4) 1.015 ____ 15. How many significant digits are there in the value 100 ? (1) one (3) three (2) two (4) an infinite number ____ 16. In multiplication and division of measured values, the measured value that determines the number of significant digits in the answer is the one that has the:
(1) largest number of significant digits (2) smallest number of significant digits (3) largest number of decimal places (4) smallest number of significant zeros
~37~
____ 17. A number written in scientific notation is made up of the: (1) significant digits of the original number (2) significant digits of the original number and 10 with an exponent (3) original number with all the digits after the decimal place is removed (4) number 10 written with an exponent equal to the number of significant digits in the original number
____ 18. The percent error is equal to 100 percent multiplied by:
____ 19. Density is equal to: (1) mass ÷ volume (3) volume ÷ mass (2) mass – volume (4) mass + volume ____ 20. In a graph, the variable that ranges along the horizontal, or x, axis is the: (1) independent (2) dependent
(1)
(2)
(3)
(4)
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Figure 1‐2
____ 21. In figure 1‐2, how should the length indicated by the arrow along the ruler be recorded? (1) 0.3 cm (3) 0.35 cm (2) 0.4 cm (4) 0.350 cm ____ 22. What metric unit is indicated by each of the shortest lines on the ruler in Figure 1‐2? (1) centimeter (3) millimeter (2) micrometer (4) one‐sixteenth inch ____ 23. In Figure 1‐2, how should the volume reading for the water be recorded? (1) 7.00 cm3 (3) 8.00 cm3 (2) 7.0 cm3 (4) 8.0 cm3 ____ 24. What metric unit is indicated by each of the lines on the graduated cylinder in Figure 1‐2? (1) centimeter (3) liter (2) cubic centimeter (4) cubic meter
~39~
MASS OF SAMPLE 4078 Team 1 Team 2 Team 3 Team 4
Reading 1 42 g 41.04 g 31.33 g 42.34 g
Reading 2 42.158 g 39.77 g 31.30 g 41.12 g
Reading 3 42.07 g 43.15 g 31.36 g 41.21 g
Average 42.1 g 41.32 g 31.33 g 41.55 g
Accepted measure from issuing lab: 41.33 g Percent error 1.9% –0.02% –24.2% 0.53%
Figure 1‐3
____ 25. Why might the measurements from Team 1 in figure 1‐3 be thought to be from different instruments?
(1) each measurement is taken to a different level of precision (2) the values of the readings are so far apart (3) the percent error is so large (4) the percent error is positive
____ 26. Which team in Figure 1‐3 is most accurate? (1) team 1 (3) team 3 (2) team 2 (4) team 4 ____ 27. Which team in Figure 1‐3 is most precise? (1) team 1 (3) team 3 (2) team 2 (4) team 4 ____ 28. In Figure 1‐3, how many significant figures should be recorded in Team 1’s average? ____ 29. In Figure 1‐3, what is Team 2’s average written in scientific notation? (1) 41.32 g (3) 4.1 x 1032 g (2) 41 x 1032 g (4) 4.132 x 101 g
~40~
Figure 1‐4
____ 30. In Figure 1‐4, what is the temperature at 3.0 minutes? (1) 0.7°C (3) 17.5°C (2) 15°C (4) 20°C ____ 31. In Figure 1‐4, at what time is the temperature equal to 35°C? (1) 6.5 minutes (3) 7.5 minutes (2) 7.0 minutes (4) 8.0 minutes ____ 32. Assuming that the relationship between the variables in Figure 1‐4 continues in the same way, what should the temperature be at 12.0 minutes? (1) 45°C (3) 55°C (2) 50°C (4) 60°C ____ 33. What is a good title for the graph in Figure 1‐4?
(1) Conversion of Water (2) Dimensional Analysis of Water (3) Cooling of a Substance (4) Heating of a Substance
~41~
PROBLEM SOLVING Use the skills you have developed in this chapter to solve each problem. 34. Express 4.5 millimeters in meters. 35. Convert 12.1 kilograms to grams. 36. Express 3.56 Mg in µg 37. Each of four students separately makes four measurements of the mass of the same object. The readings are as follows:
Student 1: 9.1 g, 9.2 g, 9.1 g, 9.1 g Student 2: 11 g, 9 g, 9 g, 11 g Student 3: 14.1 g, 11.0 g, 17.4 g, 18.8 g Student 4: 10.1 g, 9.9 g, 10.0 g, 10.0 g.
The real value of the object's mass is 10.0 g. Evaluate each student's set of readings in terms of precision and accuracy.
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38. Calculate the volume of a rectangular pan that is 27.0 cm long, 14.55 cm wide, and 9.3 cm high. (Remember to retain only significant digits in your final answer and to express your answer in the proper units.) 39. A student measures the mass of an object as 135.80 g. Calculate the percent error in the measurement, given that the accepted value for the mass is 137.23 g. 40. Find the measured mass of a sample if the accepted value is 20 grams and the percent error is 2 percent. 41. Calculate the density of an object that occupies 17.1 cm3 and has a mass of 39.26 g. Will that object float in water, given that the density of water is 1.00 g/cm3? Explain your answer.
~43~
42. Convert 73.0 seconds to weeks. Express your answer in scientific notation. 43. Calculate how many meters are in one mile (39.37 inches = 1 meter, 5286 feet = 1 mile). Express your answer in scientific notation. 44. Convert a height of 5 feet, 6 inches to meters. (2.54 cm = 1 in.)