We use dimensional analysis as a fail proof process to convert from one unit to another.
Dimensional Analysis
Using Dimensional Analysis, start with the given amount and obtain the end amount by using conversion factors.
Dimensional Analysis Example 1
If the distance between Washington, D.C. and New York City is 224.9 miles, determine the distance in centimeters.
Lipitor, a pharmaceutical drug that has been shown to lower “bad” cholesterol levels, while boosting “good” cholesterol levels had over $12 billion in sales last year. Each pill weighs 2.5 g, which contains 4.0% of the active ingredient by mass. What mass in kg of the active ingredient is present in one bottle of 120 pills?
- Consider the jar of jelly beans in the photo. To get an estimate of the number of beans in the jar you weigh s...
- A person runs at a pace of 6.52 mi/hr. How long does it take the person to run a 15.0 km race? (1 mi = 1.61 km...
- The radius of an atom of tungsten (W) is about 2.10 A . (c) If the atom is assumed to be a sphere, what is the...
- The radius of an atom of tungsten (W) is about 2.10 A . (b) How many tungsten atoms would have to be lined up ...
- The radius of an atom of tungsten (W) is about 2.10 A . (a) Express this distance in nanometers (nm).
- The radius of an atom of copper (Cu) is about 140 pm. (c) If you assume that the Cu atom is a sphere, what is...
- If Avogadro’s number of pennies is divided equally among the 321 million men, women, and children in the Unite...
- The Ogallala aquifer described in the Closer Look box in Section 18.3, provides 82% of the drinking water for ...
- The physical fitness of athletes is measured by “VO2 max,” which is the maximum volume of oxygen consumed by a...
- The estimated concentration of gold in the oceans is 1.0 * 10^-11 g/mL. (b) Assuming that the volume of the oc...
- (d) Bamboo can grow up to 60.0 cm/day. Convert this growth rate into inches per hour.
- (b) The lung capacity of the blue whale is 5.0 * 103 L. Convert this volume into gallons.
- (a) A bumblebee flies with a ground speed of 15.2 m/s. Calculate its speed in km/hr.
- (a) The speed of light in a vacuum is 2.998 * 108 m>s. Calculate its speed in miles per hour.
- (d) An individual suffering from a high cholesterol level in her blood has 242 mg of cholesterol per 100 mL o...
- (c) The Vehicle Assembly Building at the Kennedy Space Center in Florida has a volume of 3,666,500 m3. Convert...
- (b) The Sears Tower in Chicago is 1454 ft tall. Calculate its height in meters.
- Perform the following conversions: (f) 0.02500 ft3 to cm3.
- Perform the following conversions: (e) 22.50 gal/min to L/s
- Perform the following conversions: (d) 0.510 in./ms to km/hr
- Perform the following conversions: (c) $1.89/gal to dollars per liter
- Perform the following conversions: (b) 0.0550 mi to m
- Perform the following conversions: (a) 5.00 days to s
- Carry out the following conversions: (e) $3.99/lb to dollars per kg
- Carry out the following conversions: (d) 1.955 m3 to yd3
- Carry out the following conversions: (a) 0.105 in. to mm
- (a) How many liters of wine can be held in a wine barrel whose capacity is 31 gal?
- (c) If an automobile is able to travel 400 km on 47.3 L of gasoline, what is the gas mileage in miles per gall...
- (d) When the coffee is brewed according to directions, a pound of coffee beans yields 50 cups of coffee 14 cup...
- (b) The recommended adult dose of Elixophyllin®, a drug used to treat asthma, is 6 mg/kg of body mass. Calcula...
- Complete the table. a. 355 km>s _____cm>s _____m>ms b. 1228 g>l _____g>ml _____kg>ml c. 554 ...
- (d) In March 1989, the Exxon Valdez ran aground and spilled 240,000 barrels of crude petroleum off the coast o...
- (a) If an electric car is capable of going 225 km on a single charge, how many charges will it need to travel ...
- Complete the table. a. 355 km>s _____cm>s _____m>ms b. 1228 g>l _____g>ml _____kg>ml c. 554 ...
- Gold can be hammered into extremely thin sheets called gold leaf. An architect wants to cover a 30 m * 25 m ce...
- What is the volume in L of a cube with an edge length of 7.0 dm?
- What is the volume in mL of a cube with an edge length of 2.5 cm?
- The distance from Earth to the Moon is approximately 240,000 mi. (d) Earth travels around the Sun at an aver...
- The distance from Earth to the Moon is approximately 240,000 mi. (c) The speed of light is 3.00 * 108 m>s...
- The distance from Earth to the Moon is approximately 240,000 mi. (a) What is this distance in meters?
- The distance from Earth to the Moon is approximately 240,000 mi. (b) The peregrine falcon has been measured as...
- The U.S. quarter has a mass of 5.67 g and is approximately 1.55 mm thick. (c) How much money would this stack ...
- The U.S. quarter has a mass of 5.67 g and is approximately 1.55 mm thick. (a) How many quarters would have to ...
- In the United States, water used for irrigation is measured in acre-feet. An acre-foot of water covers an acr...
- The American Dental Association recommends that an adult female should consume 3.0 mg of fluoride (F - ) per d...
- In 1986 an electrical power plant in Taylorsville, Georgia, burned 8,376,726 tons of coal, a national record a...
- In January 2006, the New Horizons space probe was launched from Earth with the mission to perform a flyby stud...
- A 40-lb container of peat moss measures 14 * 20 * 30 in. A 40-lb container of topsoil has a volume of 1.9 gal....
- The total rate at which power is used by humans worldwide is approximately 15 TW (terawatts). The solar flux a...
- The diameter of a rubidium atom is 495 pm We will consider two different ways of placing the atoms on a surfac...
- (a) Assuming the dimensions of the nucleus and atom shown in Figure 2.10, what fraction of the volume of the a...
- Very small semiconductor crystals, composed of approximately 1000 to 10,000 atoms, are called quantum dots. ...
- A period at the end of sentence written with a graphite pen-cil has a diameter of 1 mm. If the period represen...
- Perform each unit conversion. a. 1.4 in to mm b. 116 ft to cm c. 1845 kg to lb d. 815 yd to km
- A 1/4-inch-thick lead sheet is used for protection from medi-cal X rays. If a single lead atom has a diameter ...
- Carry out the following conversions. (a) How many grams of meat are in a quarter-pound hamburger (0.25 lb)?
- Carry out the following conversions. (b) How tall in meters is the Willis Tower, formerly called the Sears To...
- Carry out the following conversions. (c) How large in square meters is the land area of Australia (2,941,526 ...
- In 2009, a team from Northwestern University and Western Washington University reported the preparation of a n...
- Perform each unit conversion. a. 1.4 in to mm b. 116 ft to cm c. 1845 kg to lb d. 815 yd to km
- Perform each unit conversion. a. 1.4 in to mm b. 116 ft to cm c. 1845 kg to lb d. 815 yd to km
- Perform each unit conversion. a. 1.4 in to mm b. 116 ft to cm c. 1845 kg to lb d. 815 yd to km
- A period at the end of sentence written with a graphite pen-cil has a diameter of 1 mm. How many carbon atoms ...
- Convert the following quantities into SI units with the correct number of significant figures. (c) 0.5521 gal
- Convert the following quantities into SI units with the correct number of significant figures. (e) 978.3 yd3
- Convert the following quantities into SI units with the correct number of significant figures. (b) 66.31 lb
- Convert the following quantities into SI units with the correct number of significant figures. (a) 5.4 in.
- Convert the following quantities into SI units with the correct number of significant figures. (d) 65 mi/h
- Convert the following quantities into SI units with the correct number of significant figures. (f) 2.380 mi^2
- A runner wants to run 10.0 km. Her running pace is 7.5 mi per hour. How many minutes must she run?
- A cyclist rides at an average speed of 18 mi per hour. If she wants to bike 212 km, how long (in hours) must s...
- The world record for the women’s outdoor 20,000-meter run, set in 2000 by Tegla Loroupe, is 1:05:26.6 (seconds...
- In a sunny location, sunlight has a power density of about 1 kW/m2. Photovoltaic solar cells can convert this ...
- In the United States, the emissions limit for carbon monoxide in motorcycle engine exhaust is 12.0 g of carbon...
- A certain European automobile has a gas mileage of 17 km>L. What is the gas mileage in miles per gallon?
- The volume of water used for crop irrigation is measured in acre-feet, where 1 acre-foot is the amount of wate...
- A gas can holds 5.0 gal of gasoline. Express this quantity in cm3.
- The height of a horse is usually measured in hands instead of in feet, where 1 hand equals 1/3 ft (exactly). ...
- The height of a horse is usually measured in hands instead of in feet, where 1 hand equals 1/3 ft (exactly). ...
- Weights in England are commonly measured in stones, where 1 stone = 14 lb. What is the weight in pounds of a p...
- Concentrations of substances dissolved in solution are often expressed as mass per unit volume. For example, n...
- The average U.S. farm occupies 435 acres. How many square miles is this? (1 acre = 43,560 ft2, 1 mile = 5280 f...
- Administration of digitalis, a drug used to control atrial fibrilla-tion in heart patients, must be carefully ...
- Total U.S. farmland occupies 954 million acres. How many square miles is this? (1 acre = 43,560 ft2, 1 mi = 52...
- An acetaminophen suspension for infants contains 80 mg> 0.80 mL suspension. The recommended dose is 15 mg&g...
- Among many alternative units that might be considered as a measure of time is the shake rather than the second...
- Which is larger in each pair, and by approximately how much? (d) A centimeter or an inch
- Which is larger in each pair, and by approximately how much? (b) A mile or a kilometer
- An ibuprofen suspension for infants contains 100 mg>5.0 mL suspension. The recommended dose is 10 mg>kg ...
- The density of polystyrene, a plastic commonly used to make CD cases and transparent cups, is 0.037 lbs/in3. C...
- There are exactly 60 seconds in a minute, exactly 60 minutes in an hour, exactly 24 hours in a mean solar day,...
- Determine the number of picoseconds in 2.0 hours.
- The density of polypropylene, a plastic commonly used to make bottle caps, yogurt containers, and carpeting, i...
- A large tanker truck for carrying gasoline has a capacity of 3.4 * 104 L. (a) What is the tanker’s capacity i...
- A large tanker truck for carrying gasoline has a capacity of 3.4 * 104 L. (b) If the retail price of gasoline...
- A 1.0-ounce piece of chocolate contains 15 mg of caffeine, and a 6.0-ounce cup of regular coffee contains 105 ...
- A penny has a thickness of approximately 1.0 mm. If you stacked Avogadro’s number of pennies one on top of the...
- Consider the stack of pennies in the previous problem. How much money (in dollars) would this represent? If th...
- Answer the following questions. (a) An old rule of thumb in cooking says: “A pint’s a pound the world around.”...
- Answer the following questions. (b) There are exactly 640 acres in 1 square mile. How many square meters are i...
- A bag of Hershey’s Kisses contains the following information: Serving size: 9 pieces = 41 g Calories per servi...
- Hydrogen cyanide, HCN, is a poisonous gas. The lethal dose is approximately 300 mg HCN per kilogram of air wh...
- The source of oxygen that drives the internal combustion engine in an automobile is air. Air is a mixture of g...
- The value of the euro was recently $1.15 U.S., and the price of 1 liter of gasoline in France is 1.42 euro. Wh...
- Ocean currents are measured in Sverdrups (sv) where 1 sv = 109 m3/s. The Gulf Stream off the tip of Florida, f...
- Ocean currents are measured in Sverdrups (sv) where 1 sv = 109 m3/s. The Gulf Stream off the tip of Florida, f...
- Ocean currents are measured in Sverdrups (sv) where 1 sv = 109 m3/s. The Gulf Stream off the tip of Florida, f...
- The density of iron is 7.86 g>cm3. What is its density in pounds per cubic inch (lb>in3)?
- The element gallium (Ga) has the second-largest liquid range of any element, melting at 29.78 °C and boiling a...
- The Toyota Prius, a hybrid electric vehicle, has an EPA gas mileage rating of 52 mi>gal in the city. How ma...
- The Honda Insight, a hybrid electric vehicle, has an EPA gas mileage rating of 41 mi>gal in the city. How m...
- A sample of gaseous neon atoms at atmospheric pressure and 0 °C contains 2.69 * 1022 atoms per liter. The atom...
- The diameter of a hydrogen atom is 212 pm. Find the length in kilometers of a row of 6.02 * 1023 hydrogen atom...
- The world’s record in the 100-m dash is 9.69 s, and in the 100-yd dash it is 9.21 s. Find the speed in mi>h...
- Table salt contains 39.33 g of sodium per 100 g of salt. The U.S. Food and Drug Administration (FDA) recommend...
- A length of #8 copper wire (radius = 1.63 mm) has a mass of 24.0 kg and a resistance of 2.061 ohm per km (Ω &g...