Why is it necessary to include units when reporting scientific measurements?

Why are the number of digits reported in scientific measurements important?

Why is it necessary to include units when reporting scientific measurements?

Why is scientific notation useful?

If a measured quantity is written correctly, which digits are certain? Which are uncertain?

When do zeros count as significant digits and when don’t they count?

How many significant digits are there in exact numbers? What kinds of numbers are exact?

What limits the number of significant digits in a calculation involving only multiplication and division?

What limits the number of significant digits in a calculation involving only addition and subtraction?

What are the rules for rounding numbers?

How do we determine significant figures in calculations involving both addition / subtraction and multiplication / division?

What are the basic SI units of length, mass, and time?

List the common units of volume.

Suppose you are trying to measure the diameter of a Frisbee. What unit and prefix multiplier should you use?

What is the difference between mass and weight?

Using a metric ruler, measure these objects to the correct number of significant figures. (a) quarter (diameter) (c) notebook paper (width) (b) dime (diameter) (d) this book (width)

Using a stopwatch, measure each time to the correct number of significant figures. (a) time between your heartbeats (b) time it takes you to do the next problem (c) time between your breaths

Explain why units are important in calculations.

How are units treated in a calculation?

What is a conversion factor?

Why does the fundamental value of a quantity not change when you multiply the quantity by a conversion factor?

Write the conversion factor that converts a measurement in inches to feet. How does the conversion factor change for converting a measurement in feet to inches?

Write conversion factors for each. (a) miles to kilometers (c) gallons to liters (b) kilometers to miles (d) liters to gallons

Problem 23Q This book outlines a four-step problem-solving strategy. Describe each step and its significance. (a) Sort (b) Strategize (c) Solve (d) Check

Experienced problem solvers always consider both the value and units of their answer to a problem. Why?

Draw a solution map to convert a measurement in grams to pounds.

Draw a solution map to convert a measurement in milliliters to gallons.

Draw a solution map to convert a measurement in meters to feet.

Draw a solution map to convert a measurement in ounces to grams. (1 lb = 16 oz)

What is density? Explain why density can work as a conversion factor. Between what quantities does it convert?

Explain how you would calculate the density of a substance. Include a solution map in your explanation.

Express each number in scientific notation. (a) 0.00000000007461 m (length of a hydrogen–hydrogen chemical bond) (b) 0.0000158 mi (number of miles in an inch) (c) 0.000000632 m (wavelength of red light) (d) 0.000015 m (diameter of a human hair)

Express each number in scientific notation. (a) 0.000000001 s (time it takes light to travel 1 ft) (b) 0.143 s (time it takes light to travel around the world) (c) 0.000000000001 s (time it takes a chemical bond to undergo one vibration) (d) 0.000001 m (approximate size of a dust particle)

Express each number in decimal notation (i.e., express the number without using scientific notation). (a) \(6.022 \times 10^{23}\) (number of carbon atoms in 12.01 g of carbon) (b) \(1.6\times10^{-19}\mathrm{\ C}\) (charge of a proton in coulombs) (c) \(2.99\times10^8\mathrm{\ m}/\mathrm{s}\) (speed of light) (d) \(3.44\times10^2\mathrm{\ m}/\mathrm{s}\) (speed of sound) Equation Transcription: Text Transcription: 6.022 x 10^23 1.6 x 10^-19 C 2.99 x 10^8 m/s 3.44 x 10^2 m/s

Express each number in decimal notation (i.e., express the number without using scientific notation). (a) \(3.22 \times 10^{7}\) (b) \(7.2 \times 10^{-3}\) (c) \(1.18 \times 10^{11}\) (d) \(9.43 \times 10^{-6}\) Equation Transcription: Text Transcription: 3.22 x 10^7 7.2 x 10^-3 1.18 x 10^11 9.43 x 10^-6

Express each number in decimal notation (i.e., express the number without using scientific notation). (a) \(1.30 \times 10^{6}\) (b) \(1.1 \times 10^{-4}\) (c) \(1.9 \times 10^{2}\) (d) \(7.41 \times 10^{-10}\) Equation Transcription: Text Transcription: 1.30 x 10^6 1.1 x 10^-4 1.9 x 10^2 7.41 x 10^-10

Complete the table.

Complete the table.

Read each instrument to the correct number of significant figures. Laboratory glassware should always be read from the bottom of the meniscus (the curved surface at the top of the liquid column).

Read each instrument to the correct number of significant figures. Laboratory glassware should always be read from the bottom of the meniscus (the curved surface at the top of the liquid column).

For each measured quantity, underline the zeros that are significant and draw an \(X\) through the zeros that are not. (a) 0.005050 m (b) 0.0000000000000060 s (c) 220,103 kg (d) 0.00108 in. Equation Transcription: Text Transcription: X

For each measured quantity, underline the zeros that are significant and draw an \(X\) through the zeros that are not. (a) 0.00010320 s (b) 1,322,600,324 kg (c) 0.0001240 in. (d) 0.02061 m Equation Transcription: Text Transcription: X

How many significant figures are in each measured quantity? (a) 0.001125 m (b) 0.1125 m (c) \(1.12500\times10^4\mathrm{\ m}\) (d) 11205 m Equation Transcription: Text Transcription: 1.12500 x 10^4 m

Problem 46P How many significant figures are in each measured quantity? (a) 13001 kg (b) 13111 kg (c) 1.30 × 104 kg (d) 0.00013 kg

Correct any entries in the table that are wrong.

Correct any entries in the table that are wrong.

Round each number to four significant figures. (a) 255.98612 (b) 0.0004893222 (c) \(2.900856 \times 10^{-4}\) (d) 2,231,479 Equation Transcription: Text Transcription: 2.900856 x 10^-4

Problem 51P Round each number to three significant figures. (a) 10,776.522 (b) 4.999902 × 106 (c) 1.3499999995 (d) 0.0000344988

Round each number to three significant figures. (a) 10,776.522 (b) \(4.999902 \times 10^{6}\) (c) 1.3499999995 (d) 0.0000344988 Equation Transcription: Text Transcription: 4.999902 x 10^6

Round each number to three significant figures. (a) 65.74 (b) 65.749 (c) 65.75 (d) 65.750

Each number is supposed to be rounded to three significant figures. Correct the ones that are incorrectly rounded. (a) 42.3492 to 42.4 (b) 56.9971 to 57.0 (c) 231.904 to 232 (d) 0.04555 to 0.046

Each number is supposed to be rounded to two significant figures. Correct the ones that are incorrectly rounded. (a) \(1.249 \times 10^{3}\) to \(1.3 \times 10^{3}\) (b) \(3.999 \times 10^{2}\) to 40 (c) 56.21 to 56.2 (d) 0.009964 to 0.010 Equation Transcription: Text Transcription: 1.249 x 10^3 1.3 x 10^3 3.999 x 10^2

Round the number on the left to the number of significant figures indicated by the example in the first row. (Use scientific notation as needed to avoid ambiguity.)

Round the number on the left to the number of significant figures indicated by the example in the first row. (Use scientific notation as needed to avoid ambiguity.)

Perform each calculation to the correct number of significant figures. (a) \(4.5 \times 0.03060 \times 0.391\) (b) \(5.55 \div 8.97\) (c) \(\left(7.890 \times 10^{12}\right) \div\left(6.7 \times 10^{4}\right)\) (d) \(67.8 \times 9.8 \div 100.04\) Equation Transcription: Text Transcription: 4.5 x 0.03060 x 0.391 5.55 / 8.97 (7.890 x 10^12)(6.7 x 10^4) 67.8 x 9.8 / 100.04

Perform each calculation to the correct number of significant figures. (a) \(89.3 \times 77.0 \times 0.08\) (b) \(\left(5.01 \times 10^{5}\right) \div\left(7.8 \times 10^{2}\right)\) (c) \(4.005 \times 74 \times 0.007\) (d) \(453 \div 2.031\) Equation Transcription: Text Transcription: 89.3 x 77.0 x 10^4 (5.01 x 10^5) / (7.8 x 10^2) 4.005 x 74 x 0.007 453 / 2.031

Correct any answers that have the incorrect number of significant figures. (a) \(34.00 \times 567 \div 4.564=4.2239 \times 10^{3}\) (b) \(79.3 \div 0.004 \times 35.4=7 \times 10^{5}\) (c) \(89.763 \div 22.4581=3.997\) (d) \(\left(4.32 \times 10^{12}\right) \div\left(3.1 \times 10^{-4}\right)=1.4 \times 10^{16}\) Equation Transcription: Text Transcription: 34.00 x 567 / 4.564 = 4.2239 x 10^3 79.3 / 0.004 x 35.4 = 7 x 10^5 89.763 / 22.4581 = 3.997 (4.32 x 10^12) / (3.1 x 10^-4) = 1.4 x 10^16

Correct any answers that have the incorrect number of significant figures. (a) \(45.3254 \times 89.00205=4034.05\) (b) \(0.00740 \times 45.0901=0.334\) (c) \(49857 \div 904875=0.05510\) (d) \(0.009090 \times 6007.2=54.605\) Equation Transcription: Text Transcription: 45.3254 x 89.00205 x 4034.05 0.00740 x 45.0901 = 0.334 49857 / 904875 = 0.05510 0.009090 x 6007.2 = 54.605

Perform each calculation to the correct number of significant figures. (a) 87.6 + 9.888 + 2.3 + 10.77 (b) 43.7 - 2.341 (c) 89.6 + 98.33 - 4.674 (d) 6.99 - 5.772

Perform each calculation to the correct number of significant figures. (a) 1459.3 + 9.77 + 4.32 (b) 0.004 + 0.09879 (c) 432 + 7.3 - 28.523 (d) 2.4 + 1.777

Correct any answers that have the incorrect number of significant figures. (a) \(\left(3.8 \times 10^{5}\right)-\left(8.45 \times 10^{5}\right)=-4.7 \times 10^{5}\) (b) 0.00456 + 1.0936 = 1.10 (c) 8475.45 - 34.899 = 8440.55 (d) 908.87 - 905.34095 = 3.5291 Equation Transcription: Text Transcription: (3.84 x 10^5) - (8.45 x 10^5) = -4.7 x 10^5

Correct any answers that have the incorrect number of significant figures. (a) \(78.9+890.43-23=9.5 \times 10^{2}\) (b) 9354 - 3489.56 + 34.3 = 5898.74 (c) 0.00407 + 0.0943 = 0.0984 (d) 0.00896 - 0.007 = 0.00196 Equation Transcription: Text Transcription: 78.9 + 890.43 - 23 = 9.5 x 10^2

Problem 66P Perform each calculation to the correct number of significant figures. (a) (1.7 × 106 ÷ 2.63 × 105) + 7.33 (b) (568.99 ? 232.1) ÷ 5.3 (c) (9443 + 45 ? 9.9) × 8.1 × 106 (d) (3.14 × 2.4367) ? 2.34

Perform each calculation to the correct number of significant figures. (a) \((78.4-44.889) \div 0.0087\) (b) \((34.6784 \times 5.38)+445.56\) (c) \(\left(78.7 \times 10^{5} \div 88.529\right)+356.99\) (d) \((892 \div 986.7)+5.44\) Equation Transcription: Text Transcription: (78.4 - 44.889) / 0.0087 (34.6784 x 5.38) + 445.56 (78.7 x 10^5 / 88.529) + 356.99 (892 / 986.7) + 5.44

Correct any answers that have the incorrect number of significant figures. (a) \((78.56-9.44) \times 45.6=3152\) (b) \(\left(8.9 \times 10^{5} \div 2.348 \times 10^{2}\right)+121=3.9 \times 10^{3}\) (c) \((45.8 \div 3.2)-12.3=2\) (d) \(\left(4.5 \times 10^{3}-1.53 \times 10^{3}\right) \div 34.5=86\) Equation Transcription: Text Transcription: (78.56 - 9.44) x 45.6 = 3152 (8.9 x 10^5 / 2.348 x 10^2) + 121 = 3.9 x 10^3 (45.8 / 3.2) - 12.3 = 2 (4.5 x 10^3 - 1.53 x 10^3) / 34.5 = 86

Perform each conversion. (a) 3.55 kg to grams (b) 8944 mm to meters (c) 4598 mg to kilograms (d) 0.0187 L to milliliters

Perform each conversion. (a) 155.5 cm to meters (b) 2491.6 g to kilograms (c) 248 cm to millimeters (d) 6781 mL to liters

Perform each conversion. (a) 5.88 dL to liters (b) \(3.41\times10^{-5}\mathrm{\ g}\) to micrograms (c) \(1.01\times10^{-8}\mathrm{\ s}\) to nanoseconds (d) 2.19 pm to meters Equation Transcription: Text Transcription: 3.41 x 10^-5 g 1.01 x 10^-8 s

Perform each conversion. (a) 1.08 Mm to kilometers (b) 4.88 fs to picoseconds (c) \(7.39\times10^{11}\mathrm{\ m}\) to gigameters (d) \(1.15 \times 10^{-10}\) to picometers Equation Transcription: Text Transcription: 7.39 x 10^11 m 1.15 x 10^-10 m

Perform each conversion. (a) 22.5 in. to centimeters (b) 126 ft to meters (c) 825 yd to kilometers (d) 2.4 in. to millimeters

Perform each conversion. (a) 78.3 in. to centimeters (b) 445 yd to meters (c) 336 ft to centimeters (d) 45.3 in. to millimeters

Perform each conversion. (a) 40.0 cm to inches (b) 27.8 m to feet (c) 10.0 km to miles (d) 3845 kg to pounds

Perform each conversion. (a) 254 cm to inches (b) 89 mm to inches (c) 7.5 L to quarts (d) 122 kg to pounds

Complete the table.

A vibrating string 50.0 cm long is under a tension of 1.00 N. The results from five successive stroboscopic pictures are shown in Fig. P15.72. The strobe rate is set at 5000 flashes per minute, and observations reveal that the maximum displacement occurred at flashes 1 and 5 with no other maxima in between. (a) Find the period, frequency, and wavelength for the traveling waves on this string. (b) In what normal mode (harmonic) is the string vibrating? (c) What is the speed of the traveling waves on the string? (d) How fast is point P moving when the string is in (i) position 1 and (ii) position 3? (e) What is the mass of this string? (See Section 15.3.)

Convert \(2.255 \times 10^{10}\) g to each unit. (a) kg (b) Mg (c) mg (d) metric tons (1 metric ton = 1000 kg) Equation Transcription: Text Transcription: 2.255 x 10^10 g

Convert \(1.88 \times 10^{-6}\) to each unit. (a) mg (b) cg (c) ng (d) \(\mu \mathrm{g}\) Equation Transcription: Text Transcription: 1.88 x 10^-6 g mu g

A student loses 3.3 lb in one month. How many grams did he lose?

A student gains 1.9 lb in two weeks. How many grams did he gain?

A runner wants to run 10.0 km. She knows that her running pace is 7.5 mi/h. How many minutes must she run? Hint: Use 7.5 mi/h as a conversion factor between distance and time.

A cyclist rides at an average speed of 24 mi/h. If he wants to bike 195 km, how long (in hours) must he ride?

A recipe calls for 5.0 qt of milk. What is this quantity in cubic centimeters?

A gas can holds 2.0 gal of gasoline. What is this quantity in cubic centimeters?

Fill in the blanks. (a) \(1.0\mathrm{\ km}^2\) = ______ \(\mathrm{m}^{2}\) (b) \(1.0\mathrm{\ cm}^3\) = _______ \(\mathrm{m}^{3}\) (c) \(1.0\mathrm{\ mm}^3\) = _______ \(\mathrm{m}^{3}\) Equation Transcription: Text Transcription: 1.0 km^2 m^2 1.0 cm^3 m^3 1.0 mm^3

Fill in the blanks. (a) \(1.0\mathrm{\ ft}^2\) = _________ \(\mathrm{in.}^{2}\) (b) \(1.0\mathrm{\ yd}^2\) = _________ \(\mathrm{ft}^{2}\) (c) \(1.0\mathrm{\ m}^2\) = _________ \(\mathrm{yd}^{2}\) Equation Transcription: Text Transcription: 1.0 ft^2 in.^2 1.0 yd^2 ft^2 1.0 m^2 yd^2

The hydrogen atom has a volume of approximately \(6.2\times10^{-31}\mathrm{\ m}^3\). What is this volume in each unit? (a) cubic picometers (b) cubic nanometers (c) cubic angstroms (1 angstrom = \(10^{-10}\mathrm{\ m}\)) Equation Transcription: Text Transcription: 6.2 x 10^-31 m^3 10^-10 m

Earth has a surface area of 197 million square miles. What is its area in each unit? (a) square kilometers (b) square megameters (c) square decimeters

A house has an area of \(215\mathrm{\ m}^2\). What is its area in each unit? (a) \(\mathrm{km}^{2}\) (b) \(\mathrm{dm}^{2}\) (c) \(\mathrm{cm}^{2}\) Equation Transcription: Text Transcription: 215 m^2 km^2 dm^2 cm^2

A classroom has a volume of \(285\mathrm{\ m}^3\). What is its volume in each unit? (a) \(\mathrm{km}^{3}\) (b) \(\mathrm{dm}^{3}\) (c) \(\mathrm{cm}^{3}\) Equation Transcription: Text Transcription: 285 m^3 km^3 dm^3 cm^3

Total U.S. farmland occupies 954 million acres. How many square miles is this? (1 acre = \(43,560\mathrm{\ ft}^2\); 1 mi = 5280 ft) Equation Transcription: Text Transcription: 43,560 ft^2

The average U.S. farm occupies 435 acres. How many square miles is this? (1 acre = \(43,560\mathrm{\ ft}^2\); 1 mi = 5280 ft) Equation Transcription: Text Transcription: 43,560 ft^2

A sample of an unknown metal has a mass of 35.4 g and a volume of \(3.11\mathrm{\ cm}^3\). Calculate its density and identify the metal by comparison to Table 2.4. Equation Transcription: Text Transcription: 3.11 cm^3

A new penny has a mass of 2.49 g and a volume of \(0.349\mathrm{\ cm}^3\). Is the penny pure copper? Equation Transcription: Text Transcription: 0.349 cm^3

Glycerol is a syrupy liquid often used in cosmetics and soaps. A 2.50-L sample of pure glycerol has a mass of \(3.15\times10^3\mathrm{\ g}\). What is the density of glycerol in grams per cubic centimeter? Equation Transcription: Text Transcription: 3.15 x 10^3 g

An aluminum engine block has a volume of 4.77 L and a mass of 12.88 kg. What is the density of the aluminum in grams per cubic centimeter?

A supposedly gold crown is tested to determine its density. It displaces 10.7 mL of water and has a mass of 206 g. Could the crown be made of gold?

A vase is said to be solid platinum. It displaces 18.65 mL of water and has a mass of 157 g. Could the vase be solid platinum?

Ethylene glycol (antifreeze) has a density of \(1.11\mathrm{\ g}/\mathrm{cm}^3\). (a) What is the mass in grams of 387 mL of ethylene glycol? (b) What is the volume in liters of 3.46 kg of ethylene glycol? Equation Transcription: Text Transcription: 1.11 g/cm^3

Acetone (fingernail-polish remover) has a density of \(0.7857\mathrm{\ g}/\mathrm{cm}^3\). (a) What is the mass in grams of 17.56 mL of acetone? (b) What is the volume in milliliters of 7.22 g of acetone? Equation Transcription: Text Transcription: 0.7857 g/cm^3

A thief uses a bag of sand to replace a gold statue that sits on a weight-sensitive, alarmed pedestal. The bag of sand and the statue have exactly the same volume, 1.75 L. (Assume that the mass of the bag is negligible.) (a) Calculate the mass of each object. (density of gold = \(19.3\mathrm{\ g}/\mathrm{cm}^3\); density of sand = \(3.00\mathrm{\ g}/\mathrm{cm}^3\)) (b) Did the thief set off the alarm? Explain. Equation Transcription: Text Transcription: 19.3 g/cm^3 3.00 g/cm^3

One of the particles in an atom is the proton. A proton has a radius of approximately \(1.0 \times 10^{-13}\) cm and a mass of \(1.7 \times 10^{-24} \mathrm{~g}\). Determine the density of a proton. (Volume of a sphere = \(\frac{4}{3} \pi r^{3} ; \pi=3.14\)) Equation Transcription: 1.0 × 10-13 1.7 × 10-24 g Text Transcription: 1.0 × 10^-13 1.7 × 10^-24 g 4/3 pi r^3;=3.14

A block of metal has a volume of \(13.4 \text { in. }^{3}\) and weighs 5.14 lb. What is its density in grams per cubic centimeter? Equation Transcription: Text Transcription: 13.4 in.^3

A log is either oak or pine. It displaces 2.7 gal of water and weighs 19.8 lb. Is the log oak or pine? (density of oak = \(0.9\mathrm{\ g}/\mathrm{cm}^3\); density of pine = \(0.4\mathrm{\ g}/\mathrm{cm}^3\)) Equation Transcription: Text Transcription: 0.9 g/cm^3 0.4 g/cm^3

The density of aluminum is \(2.7 ~\mathrm {g/cm^3}\). What is its density in kilograms per cubic meter?

The density of platinum is \(21.4\mathrm{\ g}/\mathrm{cm}^3\). What is its density in pounds per cubic inch? Equation Transcription: Text Transcription: 21.4 g/cm^3

A typical backyard swimming pool holds \(150\mathrm{\ yd}^3\) of water. What is the mass in pounds of the water? Equation Transcription: Text Transcription: 150 yd^3

An iceberg has a volume of \(8975\mathrm{\ ft}^3\). What is the mass in kilograms of the iceberg? The density of ice is \(0.917\mathrm{\ g}/\mathrm{cm}^3\). Equation Transcription: Text Transcription: 8975 ft^ 0.917 g/cm^3

The mass of fuel in an airplane must be determined before takeoff. If a 747 contains 155,211 L of fuel, what is the mass of the fuel in kilograms? Assume the density of the fuel to be \(0.768\mathrm{\ g}/\mathrm{cm}^3\). Equation Transcription: Text Transcription: 0.768 g/cm^3

Honda produces a hybrid electric car called the Honda Insight. The Insight has both a gasoline-powered engine and an electric motor and has an EPA gas mileage rating of 43 mi per gallon on the highway. What is the Insight’s rating in kilometers per liter?

A backpacker carries 2.5 L of white gas as fuel for her stove. How many pounds does the fuel add to her load? Assume the density of white gas to be \(0.79\mathrm{\ g}/\mathrm{cm}^3\).

You rent a car in Germany with a gas mileage rating of 12.8 km/L. What is its rating in miles per gallon?

A car has a mileage rating of 38 mi per gallon of gasoline. How many miles can the car travel on 76.5 L of gasoline?

A hybrid SUV consumes fuel at a rate of 12.8 km/L. How many miles can the car travel on 22.5 gal of gasoline?

Block A of an unknown metal has a volume of \(125 \mathrm{~cm}^3\). Block B of a different metal has a volume of \(145 \mathrm{~cm}^3\). If block A has a greater mass than block B, what can be said of the relative densities of the two metals? (Assume that both blocks are solid.)

Block \(A\) of an unknown metal has a volume of \(125\mathrm{\ cm}^3\). Block \(B\) of a different metal has a volume of \(105\mathrm{\ cm}^3\). If block \(A\) has a greater mass than block \(B\), what can be said of the relative densities of the two metals? (Assume that both blocks are solid.) Equation Transcription: Text Transcription: A 125 cm^3 B 105 cm^3

You measure the masses and volumes of two cylinders. The mass of cylinder 1 is 1.35 times the mass of cylinder 2. The volume of cylinder 1 is 0.792 times the volume of cylinder 2. If the density of cylinder 1 is \(3.85\mathrm{\ g}/\mathrm{cm}^3\), what is the density of cylinder 2? Equation Transcription: Text Transcription: 3.85 g/cm^3

Problem 120P A bag contains a mixture of copper and lead BBs. The average density of the BBs is 9.87 g/cm3. Assuming that the copper and lead are pure, determine the relative amounts of each kind of BB.

In 1999, NASA lost a \($94\) million orbiter because one group of engineers used metric units in their calculations while another group used English units. Consequently, the orbiter descended too far into the Martian atmosphere and burned up. Suppose that the orbiter was to have established orbit at 155 km and that one group of engineers specified this distance as \(1.55 \times 10^{5} \mathrm{~m}\). Suppose further that a second group of engineers programmed the orbiter to go to \(1.55 \times 10^{5} \mathrm{ft}\). What was the difference in kilometers between the two altitudes? How low did the probe go? . Equation Transcription: 1.55 × 105 m 1.55 × 105 ft Text Transcription: $94 1.55 × 10^5 m 1.55 × 10^5 ft

In 1999, scientists discovered a new class of black holes with masses 100 to 10,000 times the mass of our sun, but occupying less space than our moon. Suppose that one of these black holes has a mass of \(1 \times 10^{3}\) suns and a radius equal to one-half the radius of our moon. What is its density in grams per cubic centimeter? The mass of the sun is \(2.0 \times 10^{30} \mathrm{~kg}\), and the radius of the moon is \(2.16 \times 10^{3} \mathrm{mi}\). (Volume of a sphere = \(\frac{4}{3} \pi r^{3}\).) Equation Transcription: 1 × 103 2.0 × 1030 kg 2.16 × 103 mi r3 Text Transcription: 1 × 10^3 2.0 × 10^30 kg 2.16 × 10^3 mi 4/3 pi r^3

A titanium bicycle frame contains the same amount of titanium as a titanium cube measuring \(6.8 cm\) on a side. Use the density of titanium to calculate the mass in kilograms of titanium in the frame. What would be the mass of a similar frame composed of iron? Equation Transcription: Text Transcription: 6.8 cm