(also, factor-label method) versatile mathematical strategy for calculations involving quantities that subjects the quantities’ units to the same mathematical operations as their numbers

(also, dimensional analysis) versatile mathematical strategy for calculations involving quantities that subjects the quantities’ units to the same mathematical operations as their numbers

unit of temperature; water freezes at 32 °F and boils at 212 °F on this scale

intensive property representing the hotness or coldness of matter

unit conversion factor

ratio of equivalent quantities expressed with different units; used to convert from one unit to a different unit

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Chemistry 2e · 1.6 Mathematical Treatment of Measurement Results

Mathematical Treatment of Measurement Results: practice problems

21 problems from the book, with its answers. Check your working, or have any of them explained to you on the whiteboard.

Exercises 57
Write conversion factors (as ratios) for the number of:
(a) yards in 1 meter
(b) liters in 1 liquid quart
(c) pounds in 1 kilogram
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Exercises 59
The label on a soft drink bottle gives the volume in two units: 2.0 L and 67.6 fl oz. Use this information to derive a conversion factor between the English and metric units. How many significant figures can you justify in your conversion factor?
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Exercises 61
Soccer is played with a round ball having a circumference between 27 and 28 in. and a weight between 14 and 16 oz. What are these specifications in units of centimeters and grams?
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Exercises 63
How many milliliters of a soft drink are contained in a 12.0-oz can?
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Exercises 65
The diameter of a red blood cell is about 3 $\times$ 10⁻⁴ in. What is its diameter in centimeters?
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Exercises 67
Is a 197-lb weight lifter light enough to compete in a class limited to those weighing 90 kg or less?
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Exercises 69
Many medical laboratory tests are run using 5.0 μL blood serum. What is this volume in milliliters?
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Exercises 71
Use scientific (exponential) notation to express the following quantities in terms of the SI base units in Table 1.2:
(a) 0.13 g
(b) 232 Gg
(c) 5.23 pm
(d) 86.3 mg
(e) 37.6 cm
(f) 54 μm
(g) 1 Ts
(h) 27 ps
(i) 0.15 mK
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Exercises 73
Gasoline is sold by the liter in many countries. How many liters are required to fill a 12.0-gal gas tank?
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Exercises 75
A long ton is defined as exactly 2240 lb. What is this mass in kilograms?
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Exercises 77
Make the conversion indicated in each of the following:
(a) the length of a soccer field, 120 m (three significant figures), to feet
(b) the height of Mt. Kilimanjaro, at 19,565 ft, the highest mountain in Africa, to kilometers
(c) the area of an 8.5- × 11-inch sheet of paper in cm²
(d) the displacement volume of an automobile engine, 161 in.³, to liters
(e) the estimated mass of the atmosphere, 5.6 × 10¹⁵ tons, to kilograms
(f) the mass of a bushel of rye, 32.0 lb, to kilograms
(g) the mass of a 5.00-grain aspirin tablet to milligrams (1 grain = 0.00229 oz)
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Exercises 81
As an instructor is preparing for an experiment, he requires 225 g phosphoric acid. The only container readily available is a 150-mL Erlenmeyer flask. Is it large enough to contain the acid, whose density is 1.83 g/mL?
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Exercises 83
A chemistry student is 159 cm tall and weighs 45.8 kg. What is her height in inches and weight in pounds?
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Exercises 85
Solve these problems about lumber dimensions.
(a) To describe to a European how houses are constructed in the US, the dimensions of “two-by-four” lumber must be converted into metric units. The thickness $\times$ width $\times$ length dimensions are 1.50 in. $\times$ 3.50 in. $\times$ 8.00 ft in the US. What are the dimensions in cm $\times$ cm $\times$ m?
(b) This lumber can be used as vertical studs, which are typically placed 16.0 in. apart. What is that distance in centimeters?
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Exercises 87
Calculate the density of aluminum if 27.6 cm³ has a mass of 74.6 g.
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Exercises 89
Calculate these masses.
(a) What is the mass of 6.00 cm³ of mercury, density = 13.5939 g/cm³?
(b) What is the mass of 25.0 mL octane, density = 0.702 g/cm³?
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Exercises 91
Calculate these volumes.
(a) What is the volume of 25 g iodine, density = 4.93 g/cm³?
(b) What is the volume of 3.28 g gaseous hydrogen, density = 0.089 g/L?
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Exercises 93
Convert the boiling temperature of gold, 2966 °C, into degrees Fahrenheit and kelvin.
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Exercises 95
Convert the temperature of the coldest area in a freezer, −10 °F, to degrees Celsius and kelvin.
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Exercises 97
Convert the boiling temperature of liquid ammonia, −28.1 °F, into degrees Celsius and kelvin.
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Exercises 99
The weather in Europe was unusually warm during the summer of 1995. The TV news reported temperatures as high as 45 °C. What was the temperature on the Fahrenheit scale?
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Key terms · 5

dimensional analysis: (also, factor-label method) versatile mathematical strategy for calculations involving quantities that subjects the quantities’ units to the same mathematical operations as their numbers
factor-label method: (also, dimensional analysis) versatile mathematical strategy for calculations involving quantities that subjects the quantities’ units to the same mathematical operations as their numbers
Fahrenheit: unit of temperature; water freezes at 32 °F and boils at 212 °F on this scale
temperature: intensive property representing the hotness or coldness of matter
unit conversion factor: ratio of equivalent quantities expressed with different units; used to convert from one unit to a different unit

Learn 1.6 on the whiteboard

The tutor teaches the whole section, drawing it out step by step and answering your questions as you go.

Read 1.6 in the textbook · This section on openstax.org

Mathematical Treatment of Measurement Results: practice problems

21 problems from the book, with its answers. Check your working, or have any of them explained to you on the whiteboard.

Exercises 57

Write conversion factors (as ratios) for the number of:

(a) yards in 1 meter

(b) liters in 1 liquid quart

Exercises 59

The label on a soft drink bottle gives the volume in two units: 2.0 L and 67.6 fl oz. Use this information to derive a conversion factor between the English and metric units. How many significant figures can you justify in your conversion factor?

Exercises 61

Soccer is played with a round ball having a circumference between 27 and 28 in. and a weight between 14 and 16 oz. What are these specifications in units of centimeters and grams?

Exercises 63

How many milliliters of a soft drink are contained in a 12.0-oz can?

Exercises 65

The diameter of a red blood cell is about 3 $\times$ 10⁻⁴ in. What is its diameter in centimeters?

Exercises 67

Is a 197-lb weight lifter light enough to compete in a class limited to those weighing 90 kg or less?

Exercises 69

Many medical laboratory tests are run using 5.0 μL blood serum. What is this volume in milliliters?

Exercises 71

Use scientific (exponential) notation to express the following quantities in terms of the SI base units in Table 1.2:

(a) 0.13 g

(b) 232 Gg

(d) 86.3 mg

(e) 37.6 cm

(f) 54 μm

(g) 1 Ts

(h) 27 ps

(i) 0.15 mK

Exercises 73

Gasoline is sold by the liter in many countries. How many liters are required to fill a 12.0-gal gas tank?

Exercises 75

A long ton is defined as exactly 2240 lb. What is this mass in kilograms?

Exercises 77

Make the conversion indicated in each of the following:

(a) the length of a soccer field, 120 m (three significant figures), to feet

(b) the height of Mt. Kilimanjaro, at 19,565 ft, the highest mountain in Africa, to kilometers

(d) the displacement volume of an automobile engine, 161 in.³, to liters

(e) the estimated mass of the atmosphere, 5.6 × 10¹⁵ tons, to kilograms

(f) the mass of a bushel of rye, 32.0 lb, to kilograms

(g) the mass of a 5.00-grain aspirin tablet to milligrams (1 grain = 0.00229 oz)

Exercises 81

As an instructor is preparing for an experiment, he requires 225 g phosphoric acid. The only container readily available is a 150-mL Erlenmeyer flask. Is it large enough to contain the acid, whose density is 1.83 g/mL?

Exercises 83

A chemistry student is 159 cm tall and weighs 45.8 kg. What is her height in inches and weight in pounds?

Exercises 85

Solve these problems about lumber dimensions.

(a) To describe to a European how houses are constructed in the US, the dimensions of “two-by-four” lumber must be converted into metric units. The thickness $\times$ width $\times$ length dimensions are 1.50 in. $\times$ 3.50 in. $\times$ 8.00 ft in the US. What are the dimensions in cm $\times$ cm $\times$ m?

(b) This lumber can be used as vertical studs, which are typically placed 16.0 in. apart. What is that distance in centimeters?

Exercises 87

Calculate the density of aluminum if 27.6 cm³ has a mass of 74.6 g.

Exercises 89

Calculate these masses.

(a) What is the mass of 6.00 cm³ of mercury, density = 13.5939 g/cm³?

(b) What is the mass of 25.0 mL octane, density = 0.702 g/cm³?

Exercises 91

Calculate these volumes.

(a) What is the volume of 25 g iodine, density = 4.93 g/cm³?

(b) What is the volume of 3.28 g gaseous hydrogen, density = 0.089 g/L?

Exercises 93

Convert the boiling temperature of gold, 2966 °C, into degrees Fahrenheit and kelvin.

Exercises 95

Convert the temperature of the coldest area in a freezer, −10 °F, to degrees Celsius and kelvin.

Exercises 97

Convert the boiling temperature of liquid ammonia, −28.1 °F, into degrees Celsius and kelvin.

Exercises 99

The weather in Europe was unusually warm during the summer of 1995. The TV news reported temperatures as high as 45 °C. What was the temperature on the Fahrenheit scale?

Key terms · 5

dimensional analysis: (also, factor-label method) versatile mathematical strategy for calculations involving quantities that subjects the quantities’ units to the same mathematical operations as their numbers
factor-label method: (also, dimensional analysis) versatile mathematical strategy for calculations involving quantities that subjects the quantities’ units to the same mathematical operations as their numbers
Fahrenheit: unit of temperature; water freezes at 32 °F and boils at 212 °F on this scale
temperature: intensive property representing the hotness or coldness of matter
unit conversion factor: ratio of equivalent quantities expressed with different units; used to convert from one unit to a different unit

Learn 1.6 on the whiteboard

The tutor teaches the whole section, drawing it out step by step and answering your questions as you go.

Read 1.6 in the textbook · This section on openstax.org