Chapter 2

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

A 5-mL sample of water has a mass of 5 \(\mathrm{g} .\) What is the density of water?

The density of aluminum is 2.7 \(\mathrm{g} / \mathrm{mL} .\) What is the volume of 8.1 \(\mathrm{g}\) ?

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

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. a. 0.0045834 \(\mathrm{mm}\) \(\quad\) c. 438,904 \(\mathrm{s}\) b. 0.03054 \(\mathrm{g}\) \(\quad\) d. 7,004,300,000 \(\mathrm{g}\)

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

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. a. 5.70 g to milligrams \(\quad\) d. 45.3 \(\mathrm{mm}\) to meters b. 4.37 \(\mathrm{cm}\) to meters \(\quad\) e. 10 \(\mathrm{m}\) to centimeters c. 783 kg to grams \(\quad\) f. 37.5 \(\mathrm{g} / \mathrm{mL}\) to \(\mathrm{kg} / \mathrm{L}\)

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 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 milliliters of oxygen does each gram of hemoglobin carry?

Nutrition The recommended calcium intake for teenagers is 1300 mg per day. A glass of milk contains 305 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 \(\mathrm{mL} .\)

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 \(\mathrm{g}\) from 242.6 \(\mathrm{g},\) which value determines the number of significant figures in the answer? Explain.

Round each number to four significant figures. a. 431,801 \(\mathrm{kg} \quad\) d. 0.004384010 \(\mathrm{cm}\) b. 10,235.0 \(\mathrm{mg} \quad\) e. 0.0078100 \(\mathrm{mL}\) c. 1.0348 \(\mathrm{m} \quad\) f. 0.0098641 \(\mathrm{cg}\)

The accepted length of a steel pipe is 5.5 \(\mathrm{m} .\) 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 \(\mathrm{g} / \mathrm{mL} .\) Calculate the percent error for each of these measurements. a. 8.86 \(\mathrm{g} / \mathrm{mL} \quad\) c. 9.00 \(\mathrm{g} / \mathrm{mL}\) b. 8.92 \(\mathrm{g} / \mathrm{mL} \quad\) d. 8.98 \(\mathrm{g} / \mathrm{mL}\)

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

Gasoline Consumption 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. \(\left(4.42 \times 10^{-3} \mathrm{kg}\right) \div\left(2.0 \times 10^{2} \mathrm{kg}\right)\) 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. a. 3.01 \(\mathrm{g} \rightarrow \mathrm{cg} \quad\) d. 0.2 \(\mathrm{L} \rightarrow \mathrm{dm}^{3}\) b. 6200 \(\mathrm{m} \rightarrow \mathrm{km} \quad\) e. 0.13 \(\mathrm{cal} / \mathrm{g} \rightarrow \mathrm{kcal} / \mathrm{g}\) c. 6.24 \(\times 10^{-7} \mathrm{g} \rightarrow \mu \mathrm{g} \quad\) f. 3.21 \(\mathrm{mL} \rightarrow \mathrm{L}\)

Evaluate the following conversion. Will the answer be correct? Explain. 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-\(\mathrm{g}\) 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 \(\mathrm{g},\) and the second zinc sample had a mass of 235.10 \(\mathrm{g} .\) 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.

Three students use a meterstick with millimeter markings to measure a length of wire. Their measurements are \(3 \mathrm{cm}, 3.3 \mathrm{cm},\) and \(2.87 \mathrm{cm},\) 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? $$\begin{array}{c}{\text { mass of the Sun }=1.9891 \times 10^{30} \mathrm{kg}} \\ {\text { volume of the Moon }=2.1968 \times 10^{10} \mathrm{km}^{3}}\end{array}$$

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. a. 0.003210 \(\mathrm{g}\) \(\quad\) d. 25.38 \(\mathrm{L}\) b. 3.8754 \(\mathrm{kg}\) \(\quad\) e. 0.08763 \(\mathrm{cm}\) c. \(219,034 \mathrm{m}\) \(\quad\) f. 0.003109 \(\mathrm{mg}\)

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?

Conclude 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 \(=18.5 \mathrm{g} ;\) volume \(=15.0 \mathrm{mL}\) Liquid B: mass \(=12.8 \mathrm{g}\) ; volume \(=10.0 \mathrm{mL}\) Liquid C: mass \(=20.5 \mathrm{g}\) ; 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 \(\$ 1047 /\) troy ounce, what is the cost of the platinum in 2.00 g of this compound? A troy ounce is equal to 480 grains, and one grain is equal to 64.8 \(\mathrm{mg}\).

You record the following in your lab book: a liquid is thick and has a density of 4.58 g/mL. Which data is qualitative? Which is quantitative? (Chapter 1)

Kilogram Standard Although the standard kilogram is stored at constant temperature and humidity, unwanted matter can build up on its surface. Scientists have been looking for a more reliable standard for mass. Research and describe alternative standards that have been proposed. Find out why no alternative standard has been chosen.

Units Research and report on unusual units of measurement such as bushels, pecks, firkins, and frails.