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Sample Problem 2.1 Units of Measurement
On a typical day, a nurse encounters several situations involving measurement. State the name and type of
measurement indicated by the units in each of the following:
a. A patient has a temperature of 38.5 °C.
b. A physician orders 1.5 g of Cefuroxime for injection.
c. A physician orders 1 L of a sodium chloride solution to be given intravenously.
d. A medication is to be given to a patient every 4 h.
Solution
a.
b.
c.
d.
Degrees Celsius is a unit of temperature.
A gram is a unit of mass.
A liter is a unit of volume.
An hour is a unit of time.
Study Check 2.1
State the name and type of measurement indicated by an infant that is 32.5 cm long.
Answer
A centimeter is a unit of length
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Sample Problem 2.2 Significant Zeros
Identify the significant zeros in each of the following measured numbers:
a. 0.000 250 m
b. 70.040 g
c. 1 020 000 L
Solution
a. The zero in the last decimal place following the 5 is significant. The zeros preceding the 2 are not significant.
b. Zeros between nonzero digits or at the end of decimal numbers are significant. All the zeros in 70.040 g are
significant.
c. Zeros between nonzero digits are significant. Zeros at the end of a large number with no decimal point are
placeholders but not significant. The zero between 1 and 2 is significant, but the four zeros following the 2 are
not significant.
Study Check 2.2
Identify the significant zeros in each of the following measured numbers:
a. 0.04008 m
b. 6.00 × 103 g
Answer
a. The zeros between 4 and 8 are significant. The zeros preceding the first nonzero digit 4 are not significant.
b. All zeros in the coefficient of a number written in scientific notation are significant.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Sample Problem 2.3 Rounding Off
Round off each of the following numbers to three significant figures:
a. 35.7823 m
b. 0.002 621 7 L
c. 3.8268 × 103 g
Solution
a. To round off 35.7823 m to three significant figures, drop 823 and increase the last retained digit by 1 to give 35.8 m.
b. To round off 0.002 621 7 L to three significant figures, drop 17 to give 0.002 62 L.
c. To round off 3.8268 × 103 g to three significant figures, drop 68 and increase the last retained digit by 1 to give
3.83 × 103 g.
Study Check 2.3
Round off each of the numbers in Sample Problem 2.3 to two significant figures.
Answer
a. 36 m
b. 0.0026 L
c. 3.8 × 103 g
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Sample Problem 2.4 Significant Figures in Multiplication and Division
Perform the following calculations of measured numbers. Round off the calculator display or add zeros to give each
answer with the correct number of significant figures.
a. 56.8 × 0.37
b.
c.
b. 32
c. 5.00 (add two significant zeros)
Solution
a. 21
Study Check 2.4
Perform the following calculations of measured numbers and give the answers with the correct number of
significant figures:
a. 45.26 × 0.010 88
b. 2.6 ÷ 324
c.
Answer
a. 0.4924
b. 0.0080 or 8.0 × 10−3
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
c. 2.0
© 2016 Pearson Education, Inc.
Sample Problem 2.5 Significant Figures in Addition and Subtraction
Perform the following calculations and round off the calculator display or add zeros to give each answer with the
correct number of decimal places:
a. 104.45 mL + 0.838 mL + 46 mL
b. 153.247 g − 14.82 g
Solution
a.
b.
Study Check 2.5
Perform the following calculations and give the answers with the correct number of decimal places:
a. 82.45 mg + 1.245 mg + 0.000 56 mg
b. 4.259 L − 3.8 L
Answer
a. 83.70 mg
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
b. 0.5 L
© 2016 Pearson Education, Inc.
Sample Problem 2.6 Prefixes and Equalities
An endoscopic camera has a width of 1 mm. Complete each of the following equalities involving millimeters:
a. 1 m = _______ mm
b. 1 cm = ______ mm
Solution
a. 1 m = 1000 mm
b. 1 cm = 10 mm
Study Check 2.6
What is the relationship between millimeters and micrometers?
Answer
1 mm = 1000 μm (mcm)
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Sample Problem 2.7 Writing Conversion Factors
Identify the correct conversion factor(s) for the equality: 1 pt of blood contains 473 mL of blood.
a.
b.
c.
d.
Solution
The equality for pints and milliliters is 1 pt = 473 mL. Answers b and c are correctly written conversion factors for
the equality.
Study Check 2.7
What are the two correctly written conversion factors for the equality: 1000 mm = 1 m?
Answer
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Sample Problem 2.8 Equalities and Conversion Factors Stated in a
Problem
Write the equality and conversion factors, and identify each number as exact or give the number of significant
figures for each of the following:
a. The medication that Greg takes for his high blood pressure contains 40. mg of propranolol in 1 tablet.
b. Cold water fish such as salmon contains 1.9% omega-3 fatty acids by mass.
c. The U.S. Environmental Protection Agency (EPA) has set the maximum level for mercury in tuna at 0.5 ppm.
Solution
a. There are 40. mg of propranolol in 1 tablet.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Sample Problem 2.8 Equalities and Conversion Factors Stated in a
Problem
Continued
b. Cold water fish such as salmon contains 1.9% omega-3 fatty acids by mass.
c. The EPA has set the maximum level for mercury in tuna at 0.5 ppm.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Sample Problem 2.8 Equalities and Conversion Factors Stated in a
Problem
Continued
Study Check 2.8
Levsin (hyoscyamine), used to treat stomach and bladder problems, is available as drops with 0.125 mg Levsin per
1 mL of solution. Write the equality and its corresponding conversion factors, and identify each number as exact or
give the number of significant figures.
Answer
0.125 mg of Levsin = 1 mL of solution
The 0.125 mg is measured: It has three SFs. The 1 mL is exact.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Sample Problem 2.9 Problem Solving Using Conversion Factors
Greg’s doctor has ordered a PET scan of his heart. In radiological imaging such as PET or CT scans, dosages of
pharmaceuticals are based on body mass. If Greg weighs 144 lb, what is his body mass in kilograms?
Solution
Step 1
State the given and needed quantities.
Step 2
Write a plan to convert the given unit to the needed unit. The conversion factor relates the given unit in
the U.S. system of measurement and the needed unit in the metric system.
Step 3
State the equalities and conversion factors.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Sample Problem 2.9 Problem Solving Using Conversion Factors
Continued
Step 4
Set up the problem to cancel units and calculate the answer. Write the given, 144 lb, and multiply by the
conversion factor that has the unit lb in the denominator (bottom number) to cancel out the given unit (lb) in
the numerator.
Look at how the units cancel. The given unit lb cancels out and the needed unit kg is in the numerator. The
unit you want in the final answer is the one that remains after all the other units have canceled out. This is a
helpful way to check that you set up a problem properly.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Sample Problem 2.9 Problem Solving Using Conversion Factors
Continued
The calculator display gives the numerical answer, which is adjusted to give a final answer with the proper
number of significant figures (SFs).
The value of 65.5 combined with the unit, kg, gives the final answer of 65.5 kg. With few exceptions,
answers to numerical problems contain a number and a unit.
Study Check 2.9
A total of 2500 mL of a boric acid antiseptic solution is prepared from boric acid concentrate. How many quarts of
boric acid has been prepared?
Answer
2.6 qt
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Sample Problem 2.10 Using Two or More Conversion Factors
A doctor’s order for 0.50 g of Keflex is available as 250-mg tablets. How many tablets of Keflex are needed? In the
following setup, fill in the missing parts of the conversion factors, show the canceled units, and give the correct answer:
Solution
Study Check 2.10
A newborn has a length of 450 mm. In the following setup that calculates the baby’s length in inches, fill in the
missing parts of the conversion factors, show the canceled units, and give the correct answer:
Answer
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Sample Problem 2.11 Problem Solving Using Two Conversion Factors
Synthroid is used as a replacement or supplemental therapy for diminished thyroid function. A doctor’s order
prescribes a dosage of 0.150 mg of Synthroid. If tablets in stock contain 75 mcg of Synthroid, how many tablets
are required to provide the prescribed medication?
Solution
Step 1
State the given and needed quantities.
Step 2
Write a plan to convert the given unit to the needed unit.
Step 3
State the equalities and conversion factors.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Sample Problem 2.11 Problem Solving Using Two Conversion Factors
Continued
Step 4
Set up the problem to cancel units and calculate the answer. The problem can be set up using the metric
factor to cancel milligrams, and then the clinical factor to obtain the number of tablets as the final unit.
Study Check 2.11
A bottle contains 120 mL of cough syrup. If one teaspoon (5 mL) is given four times a day, how many days will
elapse before a refill is needed?
Answer
6 days
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Sample Problem 2.12 Using a Percentage as a Conversion Factor
A person who exercises regularly has 16% body fat by mass. If this person weighs 155 lb, what is the mass, in
kilograms, of body fat?
Solution
Step 1
State the given and needed quantities.
Step 2
Write a plan to convert the given unit to the needed unit.
Step 3
State the equalities and conversion factors.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Sample Problem 2.12 Using a Percentage as a Conversion Factor
Continued
Step 4
Set up the problem to cancel units and calculate the answer. We set up the problem using conversion factors
to cancel each unit, starting with lb of body weight, until we obtain the final unit, kg of body fat, in the
numerator.
Study Check 2.12
Uncooked lean ground beef can contain up to 22% fat by mass. How many grams of fat would be contained in 0.25 lb
of the ground beef?
Answer
25 g of fat
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Sample Problem 2.13 Problem Solving with Density
Ken, a 195-lb male patient, has a blood volume of 7.5 qt. If the density of blood is 1.06 g/mL, what is the mass,
in grams, of Ken’s blood?
Solution
Step 1
State the given and needed quantities.
Step 2
Write a plan to calculate the needed quantity.
Step 3
Write the equalities and their conversion factors including density.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Sample Problem 2.13 Problem Solving with Density
Continued
Step 4
Set up the problem to calculate the needed quantity.
Study Check 2.13
During surgery, a patient receives 3.0 pt of blood. How many kilograms of blood (density = 1.06 g/mL) were needed
for the transfusion?
Answer
1.5 kg of blood
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.