Chapter 2

SI Units What is the relationship between the SI unit for volume and the SI unit for length?

Explain how temperatures on the Celsius and Kelvin scales are related.

A 5 -mL sample of water has a mass of 5 g. What is the density of water?

The density of aluminum is 2.7 g/mL. What is the volume of 8.1 g?

An object with a mass of 7.5 g raises the level of water in a graduated cylinder from 25.1 mL to 30.1 mL. What is the density of the object?

Candy Making The directions in the candy recipe for pralines instruct the cook to remove the pot containing the candy mixture from the heat when the candy mixture reaches the soft-ball stage. The soft-ball stage corresponds to a temperature of \(236^{\circ} \mathrm{F}\) . After the soft-ball stage is reached, the pecans and vanilla are added. Can a Celsius thermometer with a range of \(-10^{\circ} \mathrm{C}\) to \(110^{\circ} \mathrm{C}\) be used to determine when the soft-ball stage is reached in the candy mixture?

How does scientific notation differ from ordinary notation?

If you move the decimal place to the left to convert a number to scientific notation, will the power of 10 be positive or negative?

When dividing numbers in scientific notation, what must you do with the exponents?

When you convert from a small unit to a large unit, what happens to the number of units?

When converting from meters to centimeters, how do you decide which values to place in the numerator and denominator of the conversion factor?

Write the following numbers in scientific notation. \(\begin{array}{ll}{\text { a. } 0.0045834 \mathrm{mm}} & {\text { c. } 438,904 \mathrm{s}} \\ {\text { b. } 0.03054 \mathrm{g}} & {\text { d. } 7,004,300,000 \mathrm{g}}\end{array}\)

Write the following numbers in ordinary notation. \(\begin{array}{ll}{\text { a. } 8.348 \times 10^{6} \mathrm{km}} & {\text { c. } 7.6352 \times 10^{-3} \mathrm{kg}} \\ {\text { b. } 3.402 \times 10^{3} \mathrm{g}} & {\text { d. } 3.02 \times 10^{-5} \mathrm{s}}\end{array}\)

Complete the following addition and subtraction problems in scientific notation. a. \(\left(6.23 \times 10^{6} \mathrm{kL}\right)+\left(5.34 \times 10^{6} \mathrm{kL}\right)\) b. \(\left(3.1 \times 10^{4} \mathrm{mm}\right)+\left(4.87 \times 10^{5} \mathrm{mm}\right)\) c. \(\left(7.21 \times 10^{3} \mathrm{mg}\right)+\left(43.8 \times 10^{2} \mathrm{mg}\right)\) d. \(\left(9.15 \times 10^{-4} \mathrm{cm}\right)+\left(3.48 \times 10^{-4} \mathrm{cm}\right)\) e. \(\left(4.68 \times 10^{-5} \mathrm{cg}\right)+\left(3.5 \times 10^{-6} \mathrm{cg}\right)\) f. \(\left(3.57 \times 10^{2} \mathrm{mL}\right)-\left(1.43 \times 10^{2} \mathrm{mL}\right)\) g. \(\left(9.87 \times 10^{4} \mathrm{g}\right)-\left(6.2 \times 10^{3} \mathrm{g}\right)\) h. \(\left(7.52 \times 10^{5} \mathrm{kg}\right)-\left(5.43 \times 10^{5} \mathrm{kg}\right)\) i. \(\left(6.48 \times 10^{-3} \mathrm{mm}\right)-\left(2.81 \times 10^{-3} \mathrm{mm}\right)\) j. \(\left(5.72 \times 10^{-4} \mathrm{dg}\right)-\left(2.3 \times 10^{-5} \mathrm{dg}\right)\)

Complete the following multiplication and division problems in scientific notation. a. \(\left(4.8 \times 10^{5} \mathrm{km}\right) \times\left(2.0 \times 10^{3} \mathrm{km}\right)\) b. \(\left(3.33 \times 10^{-4} \mathrm{m}\right) \times\left(3.00 \times 10^{-5} \mathrm{m}\right)\) c. \(\left(1.2 \times 10^{6} \mathrm{m}\right) \times\left(1.5 \times 10^{-7} \mathrm{m}\right)\) d. \(\left(8.42 \times 10^{8} \mathrm{kL}\right) \div\left(4.21 \times 10^{3} \mathrm{kL}\right)\) e. \(\left(8.4 \times 10^{6} \mathrm{L}\right) \div\left(2.4 \times 10^{-3} \mathrm{L}\right)\) f. \(\left(3.3 \times 10^{-4} \mathrm{mL}\right) \div\left(1.1 \times 10^{-6} \mathrm{mL}\right)\)

Convert the following measurements. \(\begin{array}{ll}{\text { a. } 5.70 \mathrm{g} \text { to milligrams }} & {\text { d. } 45.3 \mathrm{mm} \text { to meters }} \\ {\text { b. } 4.37 \mathrm{cm} \text { to meters }} & {\text { e. } 10 \mathrm{m} \text { to centimeters }} \\ {\text { c. } 783 \mathrm{kg} \text { to grams }} & {\text { f. } 37.5 \mathrm{g} / \mathrm{mL} \text { to } \mathrm{kg} / \mathrm{L}}\end{array}\)

Gold A troy ounce is equal to 480 grains, and 1 grain is equal to 64.8 milligrams. If the price of gold is \(\$ 560\) per troy ounce, what is the cost of 1 \(\mathrm{g}\) of gold?

Popcorn The average mass of a kernel of popcorn is 0.125 g. If 1 pound \(=16\) ounces, and 1 ounce \(=28.3 \mathrm{g},\) then how many kernels of popcorn are there in 0.500 pounds of popcorn?

Blood You have 15 g of hemoglobin in every 100 \(\mathrm{mL}\) of your blood. 10.0 \(\mathrm{mL}\) of your blood can carry 2.01 \(\mathrm{mL}\) of oxygen. How many milliters of oxygen does each gram of hemoglobin carry?

Nutrition The recommended calcium intake for teenagers is 1300 \(\mathrm{mg}\) per day. A glass of milk contains 305 \(\mathrm{mg}\) of calcium. One glass contains a volume of 8 fluid ounces. How many liters of milk should a teenager drink per day to get the recommended amount of calcium? One fluid ounce equals 29.6 mL.

Which zero is significant in the number \(50,540 ?\) What is the other zero called?

Why are percent error values never negative?

Which number will produce the same number when rounded to three significant figures: 3.456, 3.450, or 3.448?

When subtracting 61.45 g from 242.6 g, which value determines the number of significant figures in the answer? Explain.

Round each number to four significant figures. \(\begin{array}{ll}{\text { a. } 431,801 \mathrm{kg}} & {\text { d. } 0.004384010 \mathrm{cm}} \\ {\text { b. } 10,235.0 \mathrm{mg}} & {\text { e. } 0.00078100 \mathrm{mL}} \\ {\text { c. } 1.0348 \mathrm{m}} & {\text { f. } 0.0098641 \mathrm{cg}}\end{array}\)

The accepted length of a steel pipe is 5.5 m. Calculate the percent error for each of these measurements a. 5.2 \(\mathrm{m} \quad\) b. 5.5 \(\mathrm{m} \quad\) c. 5.7 \(\mathrm{m} \quad\) d. 5.1 \(\mathrm{m}\)

The accepted density for copper is 8.96 g/mL. Calculate the percent error for each of these measurements. \(\begin{array}{ll}{\text { a. } 8.86 \mathrm{g} / \mathrm{mL}} & {\text { c. } 9.00 \mathrm{g} / \mathrm{mL}} \\ {\text { b. } 8.92 \mathrm{g} / \mathrm{mL}} & {\text { d. } 8.98 \mathrm{g} / \mathrm{mL}}\end{array}\)

Which type of graph would you use to depict how many households heat with gas, oil, or electricity? Explain

Which type of graph would you choose to depict gasoline consumption over a 10-year period? Explain.

How can you find the slope of a line graph?

Complete these problems in scientific notation. Round to the correct number of significant figures. a. \(\left(5.31 \times 10^{-2} \mathrm{cm}\right) \times\left(2.46 \times 10^{5} \mathrm{cm}\right)\) b. \(\left(3.78 \times 10^{3} \mathrm{m}\right) \times\left(7.21 \times 10^{2} \mathrm{m}\right)\) c. \(\left(8.12 \times 10^{-3} \mathrm{m}\right) \times\left(1.14 \times 10^{-5} \mathrm{m}\right)\) d. \(\left(9.33 \times 10^{4} \mathrm{mm}\right) \div\left(3.0 \times 10^{2} \mathrm{mm}\right)\) e. \(\left(4.42 \times 10^{-3} \mathrm{kg}\right) \div\left(2.0 \times 10^{2} \mathrm{kg}\right)\) \(\mathrm{f}\left(6.42 \times 10^{-2} \mathrm{g}\right) \div\left(3.21 \times 10^{-3} \mathrm{g}\right)\)

Convert each quantity to the indicated units. \(\begin{array}{ll}{\text { a. } 3.01 \mathrm{g} \rightarrow \mathrm{cg}} & {\text { d. } 0.2 \mathrm{L} \rightarrow \mathrm{dm}^{3}} \\ {\text { b. } 6200 \mathrm{m} \rightarrow \mathrm{km}} & {\text { e. } 0.13 \mathrm{cal} / \mathrm{g} \rightarrow \mathrm{kcal} / \mathrm{g}} \\ {\text { c. } 6.24 \times 10^{-7} \mathrm{g} \rightarrow \mu \mathrm{g}} & {\text { f. } 3.21 \mathrm{mL} \rightarrow \mathrm{L}}\end{array}\)

Students used a balance and a graduated cylinder to collect the data shown in Table \(2.6 .\) Calculate the density of the sample. If the accepted density of this sample is 6.95 \(\mathrm{g} / \mathrm{mL}\) , calculate the percent error. \(\begin{array}{ll}{\text { Mass of sample }} & {20.46 \mathrm{g}} \\ {\text { Volume of water }} & {40.0 \mathrm{mL}} \\ {\text { Volume of water }+\text { sample }} & {43.0 \mathrm{mL}}\end{array}\)

Evaluate the following conversion. Will the answer be correct? Explain. $$\text { rate }=\frac{75 \mathrm{m}}{1 \mathrm{s}} \times \frac{60 \mathrm{s}}{1 \mathrm{min}} \times \frac{1 \mathrm{h}}{60 \mathrm{min}}$$

You have a 23 -g sample of ethanol with a density of 0.7893 \(\mathrm{g} / \mathrm{mL}\) . What volume of ethanol do you have?

Zinc Two separate masses of zinc were measured on a laboratory balance. The first zinc sample had a mass of 210.10 g, and the second zinc sample had a mass of 235.10 g. The two samples were combined. The volume of the combined sample was found to be 62.3 \(\mathrm{mL}\) . Express the mass and density of the zinc sample in the correct number of significant figures.

What mass of lead (density 11.4 \(\mathrm{g} / \mathrm{cm}^{3}\) ) would have a volume identical to 15.0 \(\mathrm{g}\) of mercury (density 13.6 \(\mathrm{g} / \mathrm{cm}^{3} ) ?\)

Three students use a meterstick with millimeter markings to measure a length of wire. Their measurements are 3 cm, 3.3 cm, and 2.87 cm, respectively. Explain which answer was recorded correctly

Astronomy The black hole in the M82 galaxy has a mass about 500 times the mass of the Sun. It has about the same volume as the Moon. What is the density of this black hole? mass of the Sun = \(1.9891 \times 10^{30} \mathrm{kg}\) volume of the Moon \(=2.1968 \times 10^{10} \mathrm{km}^{3}\)

When multiplying 602.4 \(\mathrm{m}\) by \(3.72 \mathrm{m},\) which value determines the number of significant figures in the answer? Explain.

Round each figure to three significant figures. \(\begin{array}{ll}{\text { a. } 0.003210 \mathrm{g}} & {\text { d. } 25.38 \mathrm{L}} \\ {\text { b. } 3.8754 \mathrm{kg}} & {\text { e. } 0.08763 \mathrm{cm}} \\ {\text { c. } 219,034 \mathrm{m}} & {\text { f. } 0.003109 \mathrm{mg}}\end{array}\)

Graph the data in Table \(2.7,\) with the volume on the \(x\) -axis and the mass on the \(y\) -axis. Then calculate the slope of the line. \(\begin{array}{ll}{\text {Volume (mL)}} & {\text {Mass (g)}} \\ {2.0} & {5.4} \\\ {4.0} & {10.8} \\ {6.0} & {16.2} \\ {8.0 } & {21.6} \\ {10.0} & {27.0}\end{array}\)

Cough Syrup A common brand of cough syrup comes in a 4 -fluid ounce bottle. The active ingredient in the cough syrup is dextromethorphan. For an adult, the standard dose is 2 teaspoons, and a single dose contains 20.0 \(\mathrm{mg}\) of dextromethorphan. Using the relationships, 1 fluid ounce \(=29.6 \mathrm{mL}\) and 1 teaspoon = 5.0 \(\mathrm{mL}\) determine how many grams of dextromethorphan are contained in the bottle.

Infer Which of these measurements was made with the most precise measuring device: \(8.1956 \mathrm{m}, 8.20 \mathrm{m},\) or 8.196 \(\mathrm{m}\) ? Explain your answer.

Apply When subtracting or adding two numbers in scientific notation, why do the exponents need to be the same?

Compare and Contrast What advantages do SI units have over the units commonly used in the United States? Are there any disadvantages to using SI units?

Infer Why does knowing the mass of an object not help you identify what material the object is made from?

Why might property owners hire a surveyor to determine property boundaries rather than measure the boundaries themselves?

Predict Four graduated cylinders each contain a different liquid: A, B, C, and D. Liquid A: mass \(=18.5\) g; volume \(=15.0 \mathrm{mL}\) Liquid B: mass \(=12.8\) g; volume \(=10.0 \mathrm{mL}\) Liquid C: mass \(=20.5\) g; volume \(=12.0 \mathrm{mL}\) Liquid D: mass \(=16.5 \mathrm{g} ;\) volume \(=8.0 \mathrm{mL}\) Examine the information given for each liquid, and predict the layering of the liquids if they were carefully poured into a larger graduated cylinder.

Carboplatin \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{N}_{2} \mathrm{O}_{4} \mathrm{Pt}\right)\) is a platinum-containing compound that is used to treat certain forms of cancer. This compound contains 52.5\(\%\) platinum. If the price for platinum is \(\$ 1047 / \mathrm{troy}\) ounce, what is the cost of the platinum in 2.00 \(\mathrm{g}\) of this compound? A troy ounce is equal to 480 grains, and one grain is equal to 64.8 \(\mathrm{mg}\) .