Chapter 02
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Chapter 02 Assignment
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Chapter 02 Assignment
Due: 12:00am on Tuesday, December 12, 2023
You will receive no credit for items you complete after the assignment is due. Grading Policy
Chapter 2 Reading Question 1
Part A
Which of the following is a unit of measurement for mass? Hint 1. What are some of the possible units to measure mass?
In science and the health professions, mass is typically measured using the metric system. See Section 2.1.
ANSWER:
Correct
Chapter 2 Question 1-6 Matching
Part A
Match the type of measurement to the unit given below.
Drag the appropriate labels to their respective targets.
ANSWER:
centimeters (cm) milliliters (mL) Kelvin kilograms (kg)
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Core Chemistry Skill: Counting Significant Figures
When we report a measurement in science, we are careful to report only digits known with certainty, plus a final digit that is recognized to be uncertain. It is
important to know how to count significant figures correctly, including in numbers containing zeros.
Number
Significant figures
Explanation
23.56
4
All nonzero digits are significant.
23.560
5
Trailing zeros are significant when a decimal point is shown.
1000
1
Trailing zeros are not considered significant when no decimal point is shown.
1000.
4
Showing the decimal point indicates that the preceding zeros are significant.
500.01
5
Zeros between nonzero digits are significant.
0.0078
2
Leading zeros are not significant.
Part A
Determine the number of significant figures in the measurement 6.07 .
Express your answer numerically as an integer.
Hint 1. How many nonzero digits are in the number?
How many nonzero
digits are in the measurement 6.07 ?
Express your answer numerically as an integer.
ANSWER:
Hint 2. Classify the zero
Help
Reset
2
distance
density
volume
temperature
mass
volume
distance
mass
temperature
distance
mass
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What is the rule regarding zeros found in between two nonzero digits?
ANSWER:
ANSWER:
Correct
Part B
Determine the number of significant figures in the measurement 0.0030 .
Express your answer numerically as an integer.
Hint 1. How many nonzero digits are in the number?
How many nonzero
digits are in the measurement 0.0030 ?
Express your answer numerically as an integer.
ANSWER:
Hint 2. Classify the leading zeros
What is the rule regarding zeros at the beginning of a number?
ANSWER:
Hint 3. Classify the trailing zeros
What is the rule regarding zeros at the end of a number?
ANSWER:
ANSWER:
They are always significant.
They are never significant.
They are significant if to the right of the decimal.
They are significant if to the left of the decimal.
3
1
They are always significant.
They are never significant.
They are significant if to the left of the decimal.
They are significant if to the right of the decimal.
They are always significant.
They are never significant.
They are significant only if there is a decimal point shown in the number.
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Leading zeros are not significant. Trailing zeros are significant if there is a decimal point shown in the number.
Part C
Round the value 44.981 to three significant figures.
Express your answer numerically using three significant figures.
Hint 1. How to perform rounding
Imagine that you want to round the value 0.08206 to three significant figures.
First, identify which digits should be dropped to leave just three significant figures: 0.0820
6. Next, look at the first digit to be dropped, in this case 6.
Because this digit is 5 or greater, we round the previous digit up, giving us 0.0821.
Hence the number 0.08206 is closer to 0.0821 than it is to 0.0820.
Hint 2. Identify the digits to be dropped
When rounding 44.981 to three significant figures, which digits should be dropped?
Choose the option that has the dropped digits underlined.
ANSWER:
ANSWER:
Correct
The number 44.981 is closer to 45.0 than it is to 44.9.
Chapter 2 Reading Question 2
Part A
How many significant figures are in 73,040? Hint 1. Determining the number of significant figures. See Table 2.2.
All numbers between 1 and 9 are significant. Zeros may or may not be significant. See Section 2.2.
ANSWER:
2
44.98
1
44.9
81
44.
981
4
4.981
45.0
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Chapter 2 Question 7-14 Matching
Part A
Are the numbers in each of the following statements measured or exact?
Drag the appropriate labels to their respective targets.
ANSWER:
Correct
Chapter 2 Question 11 - Multiple Choice
Part A
Significant figures are important because they indicate
ANSWER:
2 5 4 3 Help
Reset
exact
exact
measured
exact
exact
measured
measured
measured
measured
measured
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Significant Figures in Calculations
Learning Goal:
To learn how to round an answer to the correct number of significant figures.
When we report a measurement in science, we are careful to report only digits known with certainty, plus a final digit that is recognized to be uncertain. We call this
set of digits significant figures
. Often, these numbers are used in calculations. When we use a calculator, the calculator does not automatically account for
significant figures, so we have to do so ourselves. There are some basic rules for handling significant figures in calculations, as shown in the table below and
outlined to the right.
Significant Figures in Calculations
MULTIPLICATION
DIVISION
4 s.f.
2 s.f.
2 s.f.
4 s.f.
2 s.f.
2 s.f.
ADDITION
SUBTRACTION
1 d.p.
0 d.p.
0 d.p.
1 d.p.
0 d.p.
0 d.p.
note:
s.f. stands for "significant figures"
d.p. stands for "digits to the right of the decimal point"
Multiplication and division
When multiplying or dividing, the final answer is rounded to the same number of significant figures as the measured number with the fewest significant figures.
Addition and subtraction
When adding or subtracting, the final answer is rounded to the same number of digits to the right of the decimal point as the measured number with the fewest
digits to the right of the decimal point.
Part A
Compute 3.5 4.48697. Round the answer appropriately.
Express your answer numerically using the proper number of significant figures.
Hint 1. How to approach the problem
For multiplication or division, the final answer should be rounded to the same number of significant figures as the given value with the fewest significant
figures.
Hint 2. Determine the number of significant figures in the final answer
How many significant figures should be shown in the final answer after rounding?
Express the number of significant figures as an integer.
ANSWER:
the number of digits on a calculator.
the number of measurements.
the accuracy of the conversion factor.
the precision of a measurement.
the accuracy of a measurement.
2
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ANSWER:
Correct
Because this calculation involved multiplication, the final answer must be rounded to the same number of significant figures as the measured value
with the fewest significant figures.
Part B
Compute 1240.64 / 12.5. Round the answer appropriately.
Express your answer numerically using the proper number of significant figures.
Hint 1. How to approach the problem
For multiplication or division, the final answer should be rounded to the same number of significant figures as the given value with the fewest significant
figures.
Hint 2. Determine the number of significant figures in the final answer
How many significant figures should be shown in the final answer after rounding?
Express the number of significant figures as an integer.
ANSWER:
ANSWER:
Correct
Because this calculation involved division, the final answer must be rounded to the same number of significant figures as the measured value with
the fewest significant figures.
Part C
Compute 21405.6 + 9.3456 . Round the answer appropriately.
Express your answer numerically using the proper number of significant figures.
Hint 1. How to approach the problem
Be careful! The rules for addition and subtraction differ from those for multiplication and division. For addition and subtraction, the answer should be
rounded to the same number of decimal places as the number having the fewest decimal places.
Hint 2. Determine the number of digits
How many digits to the right of the decimal point should the final answer have after rounding?
Express the number of significant figures as an integer (numeral).
ANSWER:
ANSWER:
16
3
99.3
1
21414.9
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Because this calculation involved addition, the final answer must be rounded to the same number of digits to the right of the decimal point as the
measured value with the fewest number of digits to the right of the decimal point.
Core Chemistry Skill: Using Significant Figures in Calculations
Imagine that your friend steps on a digital scale that then reads 175 . You know that this is not an exact number, and that your friend's actual weight could be
something like 175.2 , or 174.9 .
You then hand your friend a golf ball that weighs 0.1 . What will the combined weight of your friend and the golf ball be? If you were to report 175.1 as the
combined weight, you would be implying that you know the value to the tenths place, when really you only know that it's about 175 .
In mathematics, . In science, however, we tend to deal with measurements rather than exact numbers, and so to a scientist,
.
Keeping track of the significant figures in measurements will prevent you from reporting calculated answers with more precision than you can truthfully claim.
Part A
Evaluate
and round the answer appropriately.
Express your answer numerically using the appropriate number of significant figures.
Hint 1. How to approach the problem
In multiplication or division, the result carries the same number of significant figures, s.f., as the factor with the fewest significant figures. For example:
The intermediate result (
) is rounded to two significant figures to reflect the least precisely known number (
), which has two significant
figures.
Hint 2. Calculate the unrounded answer
Evaluate
Do not round the answer.
Express the unrounded answer numerically.
ANSWER:
Hint 3. Determine the number of significant figures in the answer
Based on the factors given in , to how many significant figures should the final answer be rounded?
Express your answer numerically as an integer.
Hint 1. Determine the number of significant figures in each factor
The factors , , and have ______, ______, and ______ significant figure(s), respectively.
Express your answers numerically, separated by commas.
ANSWER:
ANSWER:
9.324
1,3,2
significant figure(s)
1
significant figure(s)
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ANSWER:
Correct
In multiplication or division, the result carries the same number of significant figures, s.f., as the factor with the fewest significant figures. In this case,
The intermediate result (
) is rounded to one significant figure to reflect the least precisely known number (
), which has one significant figure.
Part B
Evaluate
and round the answer appropriately.
Express your answer numerically using the appropriate number of decimal places.
Hint 1. How to approach the problem
In addition or subtraction, the result carries the same number of decimal places as the quantity carrying the fewest decimal places. For example:
We round the intermediate answer (
) to two decimal places because the quantity with the fewest decimal places (
) has two decimal places.
Hint 2. Calculate the unrounded answer
Evaluate
Do not round the answer.
Express the unrounded answer numerically.
ANSWER:
Hint 3. Determine the number of decimal places in the answer
When is evaluated and rounded appropriately, how many digits should appear after the decimal point?
Express your answer numerically as an integer.
Hint 1. Determine the number of decimal places in each quantity
The quantities , , and have ______, ______, and ______ digit(s) after the decimal point, respectively.
Express your answers numerically, separated by commas.
ANSWER:
ANSWER:
ANSWER:
9
11.111
3,1,1
digit(s) after the decimal point
1
digit(s) after the decimal point
11.1
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Part C
Evaluate
and round the answer appropriately.
Express your answer numerically using the appropriate number of significant figures or decimal places.
Hint 1. How to approach the problem
In calculations involving both multiplication/division and addition/subtraction, do the steps according to order of operations. Determine the number of
significant figures in each intermediate answer, but don't round until the end. For example:
We do the subtraction step first:
We use the subtraction rule to determine that the intermediate answer (
) has only one significant decimal place. To avoid small errors, it is best not
to round at this point; instead, underline the least significant figure as a reminder:
We use the multiplication rule to determine that the intermediate answer (
) rounds to two significant figures (
) because it is limited by the two
significant figures in .
Hint 2. Calculate the unrounded answer
Evaluate
Do not round the answer.
Express the unrounded answer numerically.
ANSWER:
Hint 3. Identify the precision of the intermediate answer
The first step of this calculation has the following unrounded answer:
Which choice shows the least significant figure, that is, to which digit would we round if this were the final answer?
ANSWER:
ANSWER:
Correct
Key Math Skill: Rounding Off
0.662
0.7
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Chapter 02 Assignment
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The rounding off of numbers in chemistry is usually done to maintain the correct number of significant figures. The two rules for rounding off are
1. If the first digit to be dropped is 4 or less
, then it and all following digits are simply dropped from the number.
2. If the first digit to be dropped is 5 or greater
, then the last retained digit is increased by 1.
For example, rounding 17.4 to two significant figures would lead to 17, and rounding 17.6 to two significant figures would lead to 18.
You can also round to a specific place. Rounding 17.44 to the nearest tenth would lead to 17.4, and rounding 17.46 to the nearest tenth would lead to 17.5.
Part A
Sort the following numbers according to whether they should be rounded up or down when rounding to the nearest tenth (the first digit after
the decimal).
Drag the appropriate items to their appropriate bins.
Hint 1. How to approach the problem
The problem asks you to round the given values to the nearest tenth. The first digit after the decimal represents tenths (1/10), the second digit
represents hundredths (1/100), the third digit after the decimal represents thousandths (1/1000), and so on. The image below summarizes this
information.
Hint 2. Determine when to round down
Given a value of 18.7
XX
, select the value that would require that the digit 7 be rounded down.
ANSWER:
ANSWER:
18.750
18.789
18.723
18.767
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When rounding to the nearest tenth, focus on the second digit after the decimal (the hundredth). If this digit is 4 or less
, then it and all following digits
are dropped from the number. If this digit is 5 or greater
, then the last retained digit is increased by 1. Part B
Drag the answers that have been correctly rounded to the appropriate number of significant figures to their place in the table. To avoid rounding errors, start
with the unrounded value before conducting each manipulation.
Drag the appropriate labels to their respective targets.
Hint 1. Identify which digits will be dropped when rounding 12.462 to two significant figures
Which digits will be dropped from 12.462 when rounding it to two significant figures? The digits in bold and underlined signify digits that will be
dropped.
ANSWER:
Hint 2. Determine whether 12.462 should be rounded up or down when rounded to two significant figures.
Should 12.462 be rounded up or down when rounding to two significant figures? (The last three digits 462
are being dropped.)
ANSWER:
ANSWER:
Reset
Help
12.46 2
12.4 62
12. 462
1 2.462
up
down
124.77
7.086
19.48
3.1564
4.324
8878.2068
66.9318
5.83
Round up
Round down
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When rounding to a specific number of significant figures, simply identify the first digit to be dropped and determine if it is in the range of 0-4 or in the
range of 5-9. If it is the former, then to round simply drop the digit; if it is the latter, drop the digit and round the preceding digit up by 1. Chapter 2 Reading Question 4
Part A
Perform the following calculation using measured numbers and round to the correct number of significant figures:
(6.912 x 48) / 12.9 Hint 1. Significant figures in multiplication and division.
In multiplication and division, the final answer is written so that it has the same number of significant figures as the measurement with the fewest SFs.
See Section 2.3.
ANSWER:
Correct
Chapter 2 Reading Question 5
Help
Reset
25.72 25.71906977 25 26 G1
G1
G1
G2
G2
G2
G4
G4
G4
G3
G3
G3
7.96
3.622
12.47
7.966
7.0
12.4
13
3.7
14.92
14
3.63
15.0
12.5
12
12.46
7.965
7.97
8.0
3.623
3.62
3.6
14.93
15
14.9
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Chapter 02 Assignment
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Part A
Perform the following calculation using measured numbers and round your answer to the appropriate number of significant figures:
4.629 + 78.2 - 57 Hint 1. Significant figures in addition and subtraction.
In problems involving addition and subtraction, the final answer is written so that it has the same number of decimal places as the measurement with
the fewest decimal places. See Section 2.3.
ANSWER:
Correct
Chapter 2 Reading Question 3
Part A
A calculated answer is 46.273 kg. Round the answer to 3 significant figures. Hint 1. What are the rules for rounding?
First, determine the number of significant figures in your final answer. Then incorporate the rules for rounding to determine if you round up (digit to be
dropped is 5 or greater) or round down (digit to be dropped is 4 or less). See Section 2.2.
ANSWER:
Correct
Chapter 2 Question 15-22 Matching
Part A
Select the correct prefix to complete the equality.
Drag the appropriate labels to their respective targets. Note: not all labels will be used.
ANSWER:
25.8 25 25.829 26 46 kg 46.27 kg 46.2 kg 46.3 kg
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Interactive Video Quiz: Dimensional Analysis
First, launch the video below. During the video, you'll be asked a conceptual question about the example. After watching the video, answer the related questions at
the right. You can watch the video again at any point to review.
Part A
An extra-strength aspirin contains 0.500 of aspirin. How many grains is this? (1 grain = 64.8 )
Hint 1. HINT
What is the conversion factor to go from grains to ? What is the conversion factor to go from to ?
ANSWER:
Help
Reset
1×10
-12
0.001
100
0.1
1
1000
1×10
12
10
0.01
0.001
1000
10
100
1000
1×10
-12
1×10
12
1
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Part B
The conversion factor used to convert 55.6 to miles is _____
Hint 1. HINT
What is the conversion factor between miles and kilometers? 1 mile = ?? ANSWER:
Correct
Part C
The dosage of quinine when a adult takes a tablet is equivalent to _____ drug per of body weight.
Hint 1. HINT
How many micrograms (
) is in 1 milligram (
)? How many kilograms are in one pound?
ANSWER:
Correct
± Metric Conversions
The metric system uses 10 as its base of evaluation. Below is a table showing several metric prefixes and their values.
grains
32.4 grains
grains
7.72 grains
627
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Prefix
Symbol
Meaning
Value
mega
million
kilo
thousand
deci
tenth
centi
hundredth
milli
thousandth
micro
millionth
nano
billionth
Part A
How many grams are in 311 ?
Express your answer numerically in grams.
Hint 1. How to approach the problem
This problem involves the conversion from milligrams to grams. The prefix milli means . So, in other words, , which is the
same as the equality .
Hint 2. Will the number of grams be greater or smaller?
Will the number of grams be greater or smaller than the number of milligrams?
ANSWER:
Hint 3. Choose a conversion formula
Which formula will properly convert milligrams to grams?
ANSWER:
ANSWER:
Correct
Part B
How many milliliters are in 27.1 ?
Express your answer numerically in milliliters.
greater
smaller
311 = 0.311
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Hint 1. How to approach the problem
This problem involves the conversion from deciliters to milliliters. The prefix deci means , so , which is the same as the
equality . The prefix milli means , so or .
Hint 2. Will the number of milliliters be greater or smaller?
Will the number of milliliters be greater or smaller than the number of deciliters?
ANSWER:
Hint 3. Choose a conversion factor
Which of the following is the most useful conversion factor for converting deciliters to milliliters?
ANSWER:
ANSWER:
Correct
Core Chemistry Skill: Writing Conversion Factors From Equations
Measured quantities are not always in the desired units. You may be reading a recipe that calls for a pint of cream, but you only have cup measures. Even
conversions between mole and gram, or those using Avogadro’s number are essentially unit conversions. An equality is the relationship between two units that
measure the same quantity. It can be used to generate conversion factors that express the numerical relationship between two units with a ratio set equal to one. A
quantity in any unit multiplied by its conversion factor gives the equivalent quantity in another unit. For example, a kilogram contains 1000 grams (1 = 1000 ).
Therefore, you can write or to convert the numbers from one unit to another.
When solving problems using conversion factors, set up the quantities in an equation such that the common units in the numerator of the initial measurement and
denominator of the conversion factor cancel leaving only the required unit. For example, if you spend 4 hours on a project and your teacher asks for your effort in
minutes, you would want to find a conversion factor that related hours to minutes. Use the equality 60 minutes in one hour to create a conversion factor that has
hours in the denominator and minutes in the numerator:
The total amount of time has not changed; the same quantity is expressed in terms of another unit.
If you wanted to report the quantity 4 hours in seconds, you would need two steps to complete the conversion. Since the required unit is seconds, the units in hours
and minutes must be canceled. The conversion factors are set up as:
greater
smaller
27.1 = 2710
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Part A
A pharmacist reading doses needs to convert the requested dose to the units reported for each medication. Choose the conversion factors to obtain the
required units.
Drag the appropriate labels to their respective targets.
Hint 1. How to approach the problem
Start by identifying the information that you know. In each conversion, you will know the units you are starting with. Then, identify the information you
need. Here, you need to determine the conversion factor needed to calculate the same value in a new unit. You can do this by analyzing the prefix
before each unit. Recall that each prefix indicates the size of a unit. Finally, check your answer by setting up the equation and making sure that like
units cancel leaving you with the unit you want.
Hint 2. Identify the equalities for the units
You can use the prefixes before each unit to determine the relationship between the two quantities. Use the prefix before each unit to determine how
the given unit and the required unit are related.
Drag the appropriate labels to their respective targets.
ANSWER:
ANSWER:
Help
Reset
1000 grams
1000 milligrams
1/1000 gram
1/1000 milligram
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Part B
A patient requires 0.100 of a drug. The pharmacist has tablets that contain 50.0 of the drug. Choose the conversion factor that the pharmacist needs to
calculate the number of tablets required for the prescribed dosage.
Hint 1. How to approach the problem
The steps to solve problems involving conversion factors are:
1. Identify the given data and its units.
2. Identify the information required in the answer and its units.
3. Analyze the relationship(s) between the given data and the required answer, and then write the equalities and conversion factors to find
the number of tablets required for the prescribed dosage.
4. Set up the problem.
Hint 2. Identify the given and required data
Step one is to identify the given data and its units. Step two is to identify the information required in the answer and its units.
Classify the information based on whether it is given data and its units, or required in the answer and its units.
Drag the appropriate items to their respective bins.
ANSWER:
Help
Reset
1000 /1 1 / 1000 1000 /1 1 /1000 1 / 1000 1000 /1
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Hint 3. Determine the equality between and Complete the equality for gram and milligrams.
Express your answer as a decimal or a fraction.
ANSWER:
Hint 4. Determine the equality describing the amount of drug in a tablet
Complete the equality for tablet and .
Express your answer with appropriate units.
ANSWER:
ANSWER:
Correct
The number of tablets required for the prescribed dosage can be calculated as:
Reset
Help
1/1000
1 milligram =
grams
The amount of drug in 1 tablet =
50 .
Each dosage requires
tablets.
0.100 grams of drug
miligrams in tablet
50.0 tablets in prescribed dose
Data given and its units
Information required and its units
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Chapter 02 Assignment
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Part C
If the patient has to be administered with a dosage of 2 tablets for every 6 hours for 7 days, what would be the number of tablets required for the prescribed
dosage?
Express your answer as a whole number.
Hint 1. How to approach the problem
The steps to solve problems involving conversion factors are:
1. Start by identifying the information given. In this problem, the requirement is to administer 2 tablets every 6 h for 7 days.
2. Next, identify the information you need in the answer. Here, the number of tablets has to be calculated for a 7 day regimen.
3. Then, find the relationship between the given information and the information you need. Use equalities and conversion factors to set the
problem up such that common units in the numerator and denominator are canceled to retain the desired unit.
4. Finally, solve the problem and express the result in terms of the desired unit.
Hint 2. Determine the conversion factor describing a single dose
Select the conversion factor that describes the number of tablets taken for every 6 h.
ANSWER:
Hint 3. Determine the equality between hour and day
Complete the equality for hours and days.
Express your answer as a whole number.
ANSWER:
Hint 4. Determine the conversion factor describing the dose per regimen
The dose has to be administered for a regimen of 7 days, the conversion factor is
ANSWER:
ANSWER:
Correct
The conversion factors you needed to use were 7 day/1, 24 h/ day, and 2 tablets/ 6 h. You can then set up the equation as:
24
1 day =
hours
Over the seven days the patient will receive 56 tablets.
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12/11/23, 11:59 PM
Chapter 02 Assignment
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Chapter 2 Reading Question 8
Part A
A container of yogurt weighs 85 grams. How many kg is that? Hint 1. How to approach a problem.
Begin with the value given in the problem. Then use a conversion factor that allows you to change the given unit to the needed unit. See Section 2.6.
ANSWER:
Correct
Chapter 2 Reading Question 7
Part A
Which of the following is a conversion factor for the following statement? A dosage for an antibiotic is 270 mg for 50 kg of body weight. Hint 1. How to write conversion factors.
Consider the possible relationship for the units within the problem. See Section 2.5.
ANSWER:
Correct
Chapter 2 Reading Question 10
Part A
A 5.23 g sample of a metal occupies 0.27 mL. Calculate the density of the metal. 0.85 kg 85,000 kg 0.085 kg 850 kg 27 mg antibiotic / 50 kg body weight 1 dosage / 270 mg antibiotic 270 mg antibiotic / 50 kg body weight
270 mg antibiotic / 1 dosage
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Chapter 02 Assignment
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Hint 1. Definition of density.
Density is the volume of space occupied by a certain mass of sample. See Section 2.7.
ANSWER:
Correct
Score Summary:
Your score on this assignment is 89.0%.
You received 16.91 out of a possible total of 19 points.
0.052 g/mL 19 g/mL 19.3 g/mL 19.37037037 g/mL
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