Dosing Error In hospitals, medicines are given by dose.

Is the cube pictured at right made of pure aluminum? Explain your answer

What is the volume of a sample that has a mass of 20 g and a density of 4 g/mL?

Challenge A 147-g piece of metal has a density of 7.00 g/mL. A 50-mL graduated cylinder contains 20.0 mL of water. What is the final volume after the metal is added to the graduated cylinder?

Define the SI units for length, mass, time, and temperature

Describe how adding the prefix mega- to a unit affects the quantity being described.

Compare a base unit and a derived unit, and list the derived units used for density and volume.

Define the relationships among the mass, volume, and density of a material.

Apply Why does oil float on water?

Calculate Samples A, B, and C have masses of 80 g, 12 g, and 33 g, and volumes of 20 mL, 4 c m 3 , and 11 mL, respectively. Which of the samples have the same density?

Design a concept map that shows the relationships among the following terms: volume, derived unit, mass, base unit, time, and length.

Express each number in scientific notation. a. 700 c. 4,500,000 e. 0.0054 g. 0.000000076 b. 38,000 d. 685,000,000,000 f. 0.00000687 h. 0.0000000008

Challenge Express each quantity in regular notation along with its appropriate unit. a. 3.60 1 0 5 s b. 5.4 1 0 -5 g/c m 3 c. 5.060 1 0 3 km d. 8.9 1 0 10 Hz

Solve each problem, and express the answer in scientific notation. a. (5 1 0 -5) + (2 1 0 -5) c. (9 1 0 2) - (7 1 0 2) b. (7 1 0 8) - (4 1 0 8) d. (4 1 0 -12) + (1 1 0 -12)

Challenge Express each answer in scientific notation in the units indicated. a. (1.26 1 0 4 kg) + (2.5 1 0 6 g) in kg b. (7.06 g) + (1.2 1 0 -4 kg) in kg c. (4.39 1 0 5 kg) - (2.8 1 0 7 g) in kg d. (5.36 1 0 -1 kg) - (7.40 1 0 -2 kg) in g

Solve each problem, and express the answer in scientific notation. a. (4 1 0 2) (1 1 0 8) c. (6 1 0 2) (2 1 0 1) b. (2 1 0 -4) (3 1 0 2) d. (8 1 0 4) (4 1 0 1)

Challenge Calculate the areas and densities. Report the answers in the correct units. a. the area of a rectangle with sides measuring 3 1 0 1 cm and 3 1 0 -2 cm b. the area of a rectangle with sides measuring 1 1 0 3 cm and 5 1 0 -1 cm c. the density of a substance having a mass of 9 1 0 5 g and a volume of 3 1 0 -1 c m 3 d. the density of a substance having a mass of 4 1 0 -3 g and a volume of 2 1 0 -2 c m 3

Write two conversion factors for each of the following. a. a 16% (by mass) salt solution b. a density of 1.25 g/mL c. a speed of 25 m/s

Challenge What conversion factors are needed to convert: a. nanometers to meters? b. density given in g/c m 3 to a value in kg/ m 3?

Use Table 2.2 on page 33 to solve each of the following. Convert 360 s to ms.

Convert 4800 g to kg.

Convert 5600 dm to m.

Convert 72 g to mg

Convert 2.45 1 0 2 ms to s.

Convert 5 m to km.

Convert 6.800 1 0 3 cm to km

Convert 2.5 1 0 1 kg to Mg.

Challenge Write the conversion factors needed to determine the number of seconds in one year.

The speedometer at right displays a cars speed in miles per hour. What is the cars speed in km/h? (1 km = 0.62 mile)

How many seconds are in 24 h?

Challenge Vinegar is 5% acetic acid by mass and has a density of 1.02 g/mL. What mass of acetic acid, in grams, is present in 185 mL of vinegar?

Describe how scientific notation makes it easier to work with very large or very small numbers.

Express the numbers 0.00087 and 54,200,000 in scientific notation.

Write the measured distance quantities 3 1 0 -4 cm and 3 1 0 4 km in regular notation.

Write a conversion factor relating cubic centimeters and milliliters

Solve How many millimeters are there in 2.5 1 0 2 km?

Explain how dimensional analysis is used to solve problems

Apply Concepts A classmate converts 68 km to meters and gets 0.068 m as the answer. Explain why this answer is incorrect, and identify the likely source of the error.

Organize Create a flowchart that outlines when to use dimensional analysis and when to use scientific notation.

Answer the following questions using data from Table 2.3.Calculate the percent errors for Student Bs trials.

Calculate the percent errors for Student Cs trials

Challenge Based on percent error, which students trial was the most accurate? The least accurate?

Determine the number of significant figures in each measurement. 508.0 L

Determine the number of significant figures in each measurement.820,400.0 L

Determine the number of significant figures in each measurement. 1.0200 1 0 5 kg

Determine the number of significant figures in each measurement. 807,000 kg

Determine the number of significant figures in each measurement. 0.049450 s

Determine the number of significant figures in each measurement. 0.000482 mL

Determine the number of significant figures in each measurement. 3.1587 1 0 -4 g

Determine the number of significant figures in each measurement. 0.0084 mL

Challenge Write the numbers 10, 100, and 1000 in scientific notation with two, three, and four significant figures, respectively.

Round each number to four significant figures. a. 84,791 kg c. 256.75 cm b. 38.5432 g d. 4.9356 m

Challenge Round each number to four significant figures, and write the answer in scientific notation. a. 0.00054818 g c. 308,659,000 mm b. 136,758 kg d. 2.0145 mL

Add and subtract as indicated. Round off when necessary. a. 43.2 cm + 51.0 cm + 48.7 cm b. 258.3 kg + 257.11 kg + 253 kg

Challenge Add and subtract as indicated. Round off when necessary. a. (4.32 1 0 3 cm) - (1.6 1 0 6 mm) b. (2.12 1 0 7 mm) + (1.8 1 0 3 cm)

Perform the following calculations. Round the answers. 24 m 3.26 m

Perform the following calculations. Round the answers. 120 m 0.10 m

Perform the following calculations. Round the answers. 1.23 m 2.0 m

Perform the following calculations. Round the answers. 53.0 m 1.53 m

Perform the following calculations. Round the answers. 4.84 m 2.4 s

Perform the following calculations. Round the answers. 60.2 m 20.1 s

Perform the following calculations. Round the answers. 102.4 m 51.2 s

Perform the following calculations. Round the answers. 168 m 58 s

Perform the following calculations. Round the answers. Challenge (1.32 1 0 3 g) (2.5 1 0 2 c m 3)

State how a measured value is reported in terms of known and estimated digits.

Define accuracy and precision.

Identify the number of significant figures in each of these measurements of an objects length: 76.48 cm, 76.47 cm, and 76.59 cm.

Apply The object in Question 47 has an actual length of 76.49 cm. Are the measurements in Question 47 accurate? Are they precise?

Calculate the error and percent error for each measurement in Question 47.

Apply Write an expression for the quantity 506,000 cm in which it is clear that all the zeros are significant

Analyze Data Students collected mass data for a group of coins. The mass of a single coin is 5.00 g. Determine the accuracy and precision of the measurements. Number of coins 5 10 20 30 50 Mass (g) 23.2 54.5 105.9 154.5 246.2

Explain why graphing can be an important tool for analyzing data

Infer What type of data must be plotted on a graph for the slope of the line to represent density?

Relate If a linear graph has a negative slope, what can you say about the dependent variable?

Summarize What data are best displayed on a circle graph? On a bar graph?

Construct a circle graph for the composition of air: 78.08% N, 20.95% O 2 , 0.93% Ar, and 0.04% C O 2 and other gases.

Infer from Figure 2.17 how long the ozone hole lasts.

Apply Graph mass versus volume for the data given in the table. What is the slope of the line? Volume ( cm 3 ) 7.5 12 15 22 Mass (g) 24.1 38.5 48.0 70.1

Why must a measurement include both a number and a unit?

Explain why standard units of measurement are particularly important to scientists.

What role do prefixes play in the metric system?

How many meters are in one kilometer? In one decimeter?

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.

Examine the density values for several common liquids and solids given in Table 2.5. Sketch the results of an experiment that layered each of the liquids and solids in a 1000-mL graduated cylinder.

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 236F. After the soft-ball stage is reached, the pecans and vanilla are added. Can a Celsius thermometer with a range of -10C to 110C 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?

Two undefined numbers expressed in regular notation are shown below, along with the number of places the decimal must move to express each in scientific notation. If each X represents a significant figure, write each number in scientific notation. a. XXX.XX b. 0.000 000 XXX

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 mm c. 438,904 s b. 0.03054 g d. 7,004,300,000 g

Write the following numbers in ordinary notation. a. 8.348 1 0 6 km c. 7.6352 1 0 -3 kg b. 3.402 1 0 3 g d. 3.02 1 0 -5 s

Complete the following addition and subtraction problems in scientific notation. a. (6.23 1 0 6 kL) + (5.34 1 0 6 kL) b. (3.1 1 0 4 mm) + (4.87 1 0 5 mm) c. (7.21 1 0 3 mg) + (43.8 1 0 2 mg) d. (9.15 1 0 -4 cm) + (3.48 1 0 -4 cm) e. (4.68 1 0 -5 cg) + (3.5 1 0 -6 cg) f. (3.57 1 0 2 mL) - (1.43 1 0 2 mL) g. (9.87 1 0 4 g) - (6.2 1 0 3 g) h. (7.52 1 0 5 kg) - (5.43 1 0 5 kg) i. (6.48 1 0 -3 mm) - (2.81 1 0 -3 mm) j. (5.72 1 0 -4 dg) - (2.3 1 0 -5 dg)

Complete the following multiplication and division problems in scientific notation. a. (4.8 1 0 5 km) (2.0 1 0 3 km) b. (3.33 1 0 -4 m) (3.00 1 0 -5 m) c. (1.2 1 0 6 m) (1.5 1 0 -7 m) d. (8.42 1 0 8 kL) (4.21 1 0 3 kL) e. (8.4 1 0 6 L) (2.4 1 0 -3 L) f. (3.3 1 0 -4 mL) (1.1 1 0 -6 mL)

Convert the following measurements. a. 5.70 g to milligrams d. 45.3 mm to meters b. 4.37 cm to meters e. 10 m to centimeters c. 783 kg to grams f. 37.5 g/mL to kg/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 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 mL of your blood. 10.0 mL of your blood can carry 2.01 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 mL.

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

Why are percent error values never negative?

If you report two measurements of mass, 7.42 g and 7.56 g, are the measurements accurate? Are they precise? Explain your answers.

Which number will produce the same number when rounded to three significant figures: 3.456, 3.450, or 3.448? 5 2 CENTIMETERS INCHES 6 Figure 2.18

Record the measurement shown in Figure 2.18 to the correct number of significant figures

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. a. 431,801 kg d. 0.004384010 cm b. 10,235.0 mg e. 0.00078100 mL c. 1.0348 m f. 0.0098641 cg

Round the answer for each problem to the correct number of significant figures. a. (7.31 1 0 4 ) + (3.23 1 0 3 ) b. (8.54 1 0 -3 ) - (3.41 1 0 -4 ) c. 4.35 dm 2.34 dm 7.35 dm d. 4.78 cm + 3.218 cm + 5.82 cm e. 38,736 km 4784 km

The accepted length of a steel pipe is 5.5 m. Calculate the percent error for each of these measurements. a. 5.2 m b. 5.5 m c. 5.7 m d. 5.1 m

The accepted density for copper is 8.96 g/mL. Calculate the percent error for each of these measurements. a. 8.86 g/mL c. 9.00 g/mL b. 8.92 g/mL d. 8.98 g/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? Mastering Problems 12.0 10.0 8.0 6.0 4.0 2.0 0 Density (cm3) Materials Wood Water Sugar Glass Iron Lead Mercury Density Comparison Figure 2.19

Use Figure 2.19 to answer the following questions. a. Which substance has the greatest density? b. Which substance has the least density? c. Which substance has a density of 7.87 g/c m 3 ? d. Which substance has a density of 11.4 g/c m 3 ?

Complete these problems in scientific notation. Round to the correct number of significant figures. a. (5.31 1 0 -2 cm) (2.46 1 0 5 cm) b. (3.78 1 0 3 m) (7.21 1 0 2 m) c. (8.12 1 0 -3 m) (1.14 1 0 -5 m) d. (9.33 1 0 4 mm) (3.0 1 0 2 mm) e. (4.42 1 0 -3 kg) (2.0 1 0 2 kg) f. (6.42 1 0 -2 g) (3.21 1 0 -3 g)

Convert each quantity to the indicated units. a. 3.01 g cg d. 0.2 L d m 3 b. 6200 m km e. 0.13 cal/g kcal/g c. 6.24 1 0 -7 g g f. 3.21 mL L

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 g/mL, calculate the percent error. Table 2.6 Volume and Mass Data Mass of sample 20.46 g Volume of water 40.0 mL Volume of water + sample 43.0 mL

Evaluate the following conversion. Will the answer be correct? Explain. rate = _75 m 1 s _60 s 1 min _1 h 60 min

You have a 23-g sample of ethanol with a density of 0.7893 g/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 mL. Express the mass and density of the zinc sample in the correct number of significant figures.

What mass of lead (density 11.4 g/c m 3 ) would have a volume identical to 15.0 g of mercury (density 13.6 g/c m 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 1 0 30 kg volume of the Moon = 2.1968 10 10 k m 3

The density of water is 1 g/c m 3 . Use your answer from Question 107 to compare the densities of water and a black hole

When multiplying 602.4 m by 3.72 m, which value determines the number of significant figures in the answer? Explain.

Round each figure to three significant figures. a. 0.003210 g d. 25.38 L b. 3.8754 kg e. 0.08763 cm c. 219,034 m f. 0.003109 mg

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. Table 2.7 Density Data Volume (mL) Mass (g) 2.0 5.4 4.0 10.8 6.0 16.2 8.0 21.6 10.0 27.0

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 mg of dextromethorphan. Using the relationships, 1 fluid ounce = 29.6 mL and 1 teaspoon = 5.0 mL, determine how many grams of dextromethorphan are contained in the bottle.

Interpret Why does it make sense for the line in Figure 2.16a to extend to (0, 0) even though this point was not measured?

Infer Which of these measurements was made with the most precise measuring device: 8.1956 m, 8.20 m, or 8.196 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?

Hypothesize Why do you think the SI standard for time was based on the distance light travels through a vacuum?

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? Nutrition Facts Serving Size cup (29 g) Servings Per Container about 17 Amount Per Serving Calories 120 Total Fat 1g 2% Saturated Fat 1 g 5% Cholesterol 0 mg 0% Sodium 160 mg 7% Potassium 25 mg 1% Total Carbohydrate 25 g 9% Dietary Fiber less than 1 g 2% Sugars 13 g Protein 1 g Vitamin A 4% Calories from Fat 10 % Daily Value * Figure 2.20

Apply Dimensional Analysis Evaluate the breakfast cereal nutritional label shown in Figure 2.20. This product contains 160 mg of salt in each serving. If you eat 2.0 cups of cereal a day, how many grams of salt are you ingesting? What percent of your daily recommended salt intake does this represent?

Predict Four graduated cylinders each contain a different liquid: A, B, C, and D. Liquid A: mass = 18.5 g; volume = 15.0 mL Liquid B: mass = 12.8 g; volume = 10.0 mL Liquid C: mass = 20.5 g; volume = 12.0 mL Liquid D: mass = 16.5 g; volume = 8.0 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 ( C 6 H 12 N 2 O 4 Pt) 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 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.

Product Volume Research the range of volumes used for packaging liquids sold in supermarkets.

Dosing Error In hospitals, medicines are given by dose. Find out what amount of error in the administered dose is acceptable for various medicines.

How is temperature related to the density of ocean water at depths less than 1000 m?

Describe the effect of depth on salinity.

Describe how salinity changes as the ocean water cools