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**Sample Problem 1.1 Chemicals**

Why is the copper in copper wire an example of a chemical, while sunlight is not? Solution Copper is a chemical that has the same composition and properties wherever it is found. Sunlight is energy given off by the Sun. Thus, sunlight does not contain matter, which means it is not a chemical. Study Check 1.1 Which of the following are chemicals? a. iron b. tin c. a low temperature d. water The answers to all the Study Checks can be found at the end of this chapter.

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**Sample Problem 1.2 Scientific Notation**

Write each of the following in scientific notation: a m b g c. 143 mL Solution a. To write a coefficient of 7.5, which is more than 1 but less than 10, move the decimal point four places to the left to give 7.5 104 m. b. To write a coefficient of 9.8, which is more than 1 but less than 10, move the decimal point three places to the right to give 9.8 10–3g. c. To write a coefficient of 1.43, which is more than 1 but less than 10, move the decimal point two places to the left to give 1.43 102mL. Study Check 1.2 Write each of the following in scientific notation: a m b g

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**Sample Problem 1.3 Rounding Off**

Round off each of the following numbers to three significant figures: a m b L c 103 g d kg Solution a m b L c 103 g d kg Study Check 1.3 Round off each of the numbers in Sample Problem 1.3 to two significant figures.

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**Sample Problem 1.4 Significant Figures in Multiplication and Division**

Perform the following calculations of measured numbers. Give the answers with the correct number of significant figures. a b c. Solution a b c (add two significant zeros) Study Check 1.4 Perform the following calculations of measured numbers and give the answers with the correct number of significant figures: a b. 2.6 c.

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**Sample Problem 1.5 Decimal Places in Addition and Subtraction**

Perform the following calculations and give the answers with the correct number of decimal places: a cm cm b g – g Solution a cm (rounded off to one decimal place) b g (rounded off to two decimal places) Study Check 1.5 Perform the following calculations and give the answers with the correct number of decimal places: a mg mg mg b L – 3.8 L

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**Sample Problem 1.6 Prefixes**

The storage capacity for a hard disk drive (HDD) is specified using prefixes: megabyte (MB), gigabyte (GB), or terabyte (TB). Indicate the storage capacity in bytes for each of the following hard disk drives. Suggest a reason for describing a HDD storage capacity in gigabytes or terabytes. a. 5 MB b. 2 GB Solution a. The prefix mega (M) in MB is equal to or 1 106. Thus, 5 MB is equal to (5 106) bytes. b. The prefix giga (G) in GB is equal to or 1 109. Thus, 2 GB is equal to (2 109) bytes. Study Check 1.6 Hard drives now have a storage capacity of 1.5 TB. How many bytes are stored? Expressing HDD capacity in gigabytes or terabytes gives a more reasonable number to work with than a number with many zeros or a large power of 10

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**Sample Problem 1.7 Writing Metric Equalities**

Complete the following list of metric equalities: a. 1 L = ________ dL b. 1 km = ________ m c. 1 cm3 = ________ mL Solution a. 10 dL b. 1 103 m c. 1 mL Study Check 1.7 Complete each of the following equalities: a. 1 kg = ________ g b. 1 mL = ________ L

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**Sample Problem 1.8 Conversion Factors Stated in a Problem**

Write two conversion factors for each of the following statements: a. There are 325 mg of aspirin in 1 tablet. b. The EPA has set the maximum level for mercury in tuna at 0.1 ppm. Solution a and b and Study Check 1.8 What conversion factors can be written for the following statements? a. A cyclist in the Tour de France bicycle race rides at the average speed of 62.2 km/h. b. The permissible level of arsenic in water is 10 ppb.

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**Sample Problem 1.9 Problem Solving Using Metric Factors**

In radiological imaging such as PET or CT scans, dosages of pharmaceuticals are based on body mass. If a person weighs 164 lb, what is the body mass in kilograms? Solution Step 1 State the given and needed quantities. Given 164 lb Need kilograms Step 2 Write a plan to convert the given unit to the needed unit. We see that the given unit is in the U.S. system of measurement and the needed unit in the metric system. Therefore, the conversion factor must relate the U.S. unit lb to the metric unit kg. Step 3 State the equalities and conversion factors needed to cancel units.

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**Sample Problem 1.9 Problem Solving Using Metric Factors**

Continued Solution Step Set up problem to cancel units and calculate answer. Write the given, 164 lb, and set up the conversion factor with 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. The calculation gives the numerical answer, which is adjusted to give a final answer with the proper number of significant figures (SFs).

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**Sample Problem 1.9 Problem Solving Using Metric Factors**

Continued The value of 74.5 combined with the unit, kg, gives the final answer of 74.5 kg. With few exceptions, answers to numerical problems contain a number and a unit. Study Check 1.9 If 1890 mL of orange juice is prepared from orange juice concentrate, how many liters of orange juice is that?

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**Sample Problem 1.10 Problem Solving Using Two Factors**

Synthroid is used as a replacement or supplemental therapy for diminished thyroid function. A doctor’s order prescribed a dosage of mg. If tablets in stock contain 50 mg of Synthroid, how many tablets are required to provide the prescribed medication? Solution Step 1 State the given and needed quantities. Given mg of Synthroid Need number of tablets Step 2 Write a plan to convert the given unit to the needed unit. Step 3 State the equalities and conversion factors needed to cancel units. In the problem, the information for the dosage is given as 50 mg per tablet. Using this as an equality along with the metric equality for milligrams and micrograms provides the following conversion factors:

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**Sample Problem 1.10 Problem Solving Using Two Factors**

Continued Solution Step Set up problem to cancel units and calculate answer. The problem can be set up using the metric factor to cancel milligrams, and then the clinical factor to obtain tablets as the final unit. Study Check 1.10 One medium bran muffin contains 4.2 g of fiber. How many ounces (oz) of fiber are obtained by eating three medium bran muffins if 1 lb = 16 oz? (Hint: number of muffins g of fiber lb oz)

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**Sample Problem 1.11 Using a Percent as a Conversion Factor**

A person who exercises regularly has 16% body fat. If this person weighs 155 lb, what is the mass, in kilograms, of body fat? Solution Step 1 State the given and needed quantities. Given 155 lb of body weight; 16% body fat Need kilograms of body fat Step 2 Write a plan to convert the given unit to the needed unit. Step 3 State the equalities and conversion factors needed to cancel units. One equality is the U.S.– metric factor for lb and kg. The second is the percent factor derived from the percentage information given in the problem.

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**Sample Problem 1.11 Using a Percent as a Conversion Factor**

Continued Solution Step Set up problem to cancel units and calculate answer. We can 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. After we count the significant figures in the measured quantities, we write the needed answer with the proper number of significant figures. Study Check 1.11 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?

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**Sample Problem 1.12 Calculating Density**

High-density lipoprotein (HDL) contains large amounts of proteins and small amounts of cholesterol. If a g sample of HDL has a volume of cm3, what is the density of the HDL sample? Solution Step 1 State the given and needed quantities. Given mass of HDL sample = g; volume = cm3 Need density (g/cm3) Step 2 Write the density expression. Step 3 Express mass in grams and volume in milliliters (mL) or cm3. Mass of HDL sample = g Volume of HDL sample = cm3 Step Substitute mass and volume into the density expression and calculate the density. Study Check 1.12 Low-density lipoprotein (LDL) contains small amounts of proteins and large amounts of cholesterol. If a 0.380-g sample of LDL has a volume of cm3, what is the density of the LDL sample?

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**Sample Problem 1.13 Using Volume Displacement to Calculate Density**

A lead weight used in the belt of a scuba diver has a mass of 226 g. When the lead weight is placed in a graduated cylinder containing mL of water, the water level rises to mL. What is the density of the lead weight (g/mL)? Solution Step 1 State the given and needed quantities. Given mass = 226 g; water level before object submerged = mL; water level after object submerged = mL Need density (g/mL) Step 2 Write the density expression. Step 3 Express mass in grams and volume in milliliters (mL) or cm3. Mass of lead weight = 226 g The volume of the lead weight is equal to the volume of water displaced, which is calculated as follows: Water level after object submerged = mL Water level before object submerged = mL Water displaced (volume of lead weight) = 20.0 mL

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**Sample Problem 1.13 Using Volume Displacement to Calculate Density**

Continued Solution Step Substitute mass and volume into the density expression and calculate the density. The density is calculated by dividing the mass (g) by the volume (mL). Be sure to use the volume of water the object displaced and not the original volume of water. Study Check 1.13 A total of 0.50 lb of glass marbles is added to 425 mL of water. The water level rises to a volume of 528 mL. What is the density (g/mL) of the glass marbles?

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**Sample Problem 1.14 Problem Solving with Density**

John took 2.0 teaspoons (tsp) of cough syrup for a persistent cough. If the syrup had a density of 1.20 g/mL and there is 5.0 mL in 1 tsp, what was the mass, in grams, of the cough syrup? Solution Step 1 State the given and needed quantities. Given 2.0 tsp Need grams of syrup Step 2 Write a plan to calculate the needed quantity. Step 3 Write equalities and their conversion factors including density.

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**Sample Problem 1.14 Problem Solving with Density**

Continued Solution Step Set up problem to calculate the needed quantity. Study Check 1.14 How many milliliters of mercury are in a thermometer that contains 20.4 g of mercury? (See Table 1.13 for the density of mercury.)

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