Practice A Dimensional Analysis Determine if each conversion will result in a larger or smaller quantity. 1. kilometers to meters 2. ounces to quarts. months to days Convert each measure. 4. 450 grams to kilograms 5. miles to feet 6. 10 cups to pints 7. 0 quarts to gallons 8. Julie is a member of her school s bowling team. She uses a 14-pound bowling ball. How many ounces is the bowling ball? 9. In 1945 Richard James invented the Slinky. It was made of 87 feet of flat wire coiled into -inch diameter circles. How many inches of coiled flat wire were used to make the original Slinky? 10. The mantis is a long, slender green and brown insect. The Carolina mantis, a native species, can grow to 7.6 centimeters long. How many millimeters is this? 11. It is 8 kilometers from a store to a bus station. To the nearest mile, how many miles is it from the store to the bus station? 12. An orange weighs 4 ounces. How much does the orange weigh in grams? 1. A recipe needs 4 quarts of milk. How many liters of milk does the recipe need?
Practice B Dimensional Analysis Convert each measure. 1. 00 milligrams to grams 2. 500 yards to feet. 72 ounces to pints 4. 7 quarts to gallons 5. Jesse s dog Angel weighs 18 1 2 pounds. How many ounces does Angel weigh? 6. A roll of tape contains 2.9 meters of tape. How many millimeters of tape does the roll contain? 7. There are two types of lifts in the sport of weightlifting, the snatch and the clean and jerk. Winners are determined by the combined weights of the two type of lifts. In the 2002 Collegiate Weightlifting Competition, Timothy Leancu from the U.S. Naval Academy competed in the 94-kilogram weight class. He lifted 100 kg in the snatch and 12.5 kg in the clean and jerk. What was the combined weight of his lifts in grams? 8. A scientist uses 10.6 ml of blood for an experiment. How many fluid ounces of blood does the scientist use? 9. Bernard bought a table that is 100 cm long. To the nearest tenth of an inch, how long is Bernard s table? 10. On a field trip, a class picked 50 pounds of strawberries. How many kilograms of strawberries did the class pick?
Practice C Dimensional Analysis Use conversion factors to find each specified amount. 1. Homework problems solved in 2 hours 0 minutes at a rate of 26 problems an hour 2. Ice cream cones sold in the month of March at the rate of 16 a day. Miles walked in 1 hour at an average rate of 5.5 feet per second 4. Fast-food meals eaten in a month at a rate of 72 meals in a year 5. Decals produced in 8 hours at a rate of 180 decals per minute 6. Distance traveled (in feet) after 45 seconds at 60 miles per hour 7. Weight in ounces of 50 tons of metal 8. The giant clam is a sea creature that can weigh up to 227 kg. To the nearest whole number, what is the weight in ounces of the giant clam? (Hint: 2.2046 lb 1 kg) 9. The ruby-throated hummingbird is about 4 inches long and is noted for its annual nonstop migration of 500 miles across the Gulf of Mexico, and for the rapid flapping of its wings. Some hummingbirds flap their wings 55 times per second. If the ruby-throated hummingbird is only 4 inches long and migrates 500 miles, how many of the hummingbird s body lengths are equal to the distance of its migration?
Review for Mastery Dimensional Analysis A conversion relation gives equivalent units. 1 foot = 12 inches 1 week = 7 days 1 pound = 16 ounces Complete each conversion relation. 1. 1 gallon = quarts 2. 1 meter = centimeters. 1 yard = feet To change from one unit to another, multiply by a fraction of value 1. Convert 7 ft to in. Use 1 foot = 12 inches to write a fraction of value 1. Put the unit to be changed in the denominator. 7 ft 12 in. 1 ft = (7 12) in. = 84 in. 12 in. 1 ft. When converting from a larger unit to a When converting from a smaller unit to smaller, the result is a larger number. a larger, the result is a smaller number. 7 ft = 84 in. 84 in. = 7 ft Complete to convert each unit. 4. 72 inches to feet 5. 40 ounces to pounds 1 ft = 1 lb = unit for denominator of fraction is unit for denominator of fraction is 72 in. = ft 40 oz = lb 6. 75 meters to centimeters 7. 150 pounds to kilograms 1 m = 1 kg = 2.2 lb unit for denominator of fraction is unit for denominator of fraction is 75 m = cm 150 lb kg
Review for Mastery Dimensional Analysis (continued) When rates are involved, two conversions may be needed. 55 mi Convert 55 miles per hour to feet per second. First, change miles to feet. Use 1 mile = 5280 feet to write a fraction of value 1. Miles, the unit to be changed, is in the numerator of the given rate. So, put miles in the denominator of the fraction of value 1. 55 mi 5280 ft 1 mi = (55 5280) ft = 290,400 ft 5280 ft 1 mi Now, change hours to seconds. Use 1 hour = 600 seconds to write a fraction of value 1. Hours, the unit to be changed, is in the denominator of the given rate. So, put hours in the numerator of the fraction of value 1. 600 s 290,400 ft 600 s 290,400 ft = 80.7 ft 600 s s 9 7 2 6 Complete to convert the units of the given rate. 8. Convert 60 miles per hour to yards per minute. In ratio form the rate is: The conversion relation between miles and yards is: 1 mi = yd The unit miles is in the of the given rate. What place will miles take in the fraction of value 1? To convert from miles to yards: 60 mi = The conversion relation between hours and minutes is: = min The unit hours is in the of the given rate. What place will hours take in the fraction of value 1? To convert from hours to minutes: yd yd = yd min
Challenge Water, Water, Everywhere Next time you are in a supermarket, pick up a gallon of water to verify what you will now determine. How many pounds does a gallon of water weigh? The amount of space between particles of a substance is what determines its density. Lead is more dense than wood, which is more dense than foam rubber. Density d is equal to the mass (weight) m of a substance divided by its volume V. d = m V Water was used as the basis for establishing the metric unit of mass. 1 g The density of water is 1 gram per milliliter: 1 ml. 1. Use the conversion relation 1 ml = 1 cm to write the density of water in terms of grams per cubic centimeter. density of water = 2. Since 1 m = 100 cm, how many cubic centimeters are there in 1 cubic meter? 1 m = cm. Use your results from Exercises 1 and 2, and the conversion relation 1 kg = 1000 g to write the density of water in terms of kilograms per cubic meters. Round your answer to the nearest hundredth. density of water = 4. Use your result from Exercise and these conversion relations to write the density of water as a unit rate in terms of pounds per gallon: 1 kg = 2.205 lb and 1 m = 264.2 gal density of water = 5. So, a gallon of water weighs about pounds.
Problem Solving Dimensional Analysis Use the following: 1 mile = 1.609 km; 1 kg = 2.2046 lb. Round to the nearest tenth. 1. Worker bees travel up to 14 km to find pollen and nectar. How far will a worker bee travel in miles? 2. Worker bees can travel at 24 km/h. How fast can the worker bee travel in miles per hour?. The average hippopotamus weighs 1800 kg. How many pounds does the average hippopotamus weigh? 4. At the age of 45, an elephant grows teeth, each weighing 4 kg. How many pounds do these teeth weigh? Paraceratherium was the biggest land mammal there has ever been. It lived about 5 million years ago and was 8 m tall and 11 m long. It looked like a gigantic rhinoceros but had a long neck like a giraffe. 1 foot = 0.048 meters. Round to the nearest tenth. 5. How tall was the paraceratherium in feet? 6. How long was the paraceratherium in feet? Round to the nearest tenth. Choose the letter for the best answer. 7. The fastest sporting animal is the racing pigeon that flies up to 110 mi an hour. How fast is the racing pigeon in feet each second? A 75.0 ft/s C 54.2 ft/s B 161. ft/s D 9,680 ft/s 9. The average person falls asleep in seven minutes. How many seconds does it take the average person to fall asleep? A 127 s C 420 s B 85 s D 25,200 s 8. The longest gloved fight between two Americans lasted for more than seven hours before being declared a draw. How many seconds did the fight last? F 127 s H 420 s G 85 s J 25,200 s 10. The brain of an average adult male weighs 55 oz. How many pounds does the average male brain weigh? F.4 lb H 1.8 lb G 5.8 lb J 880 lb
Reading Strategies Choose Relevant Information Here are some common measurement units and their equivalents. 16 ounces in 1 pound 12 inches in 1 foot 8 ounces in 1 cup 60 minutes in 1 hour feet in 1 yard 4 quarts in 1 gallon You can change a measurement from one unit to another if you know the equivalent measure. If a larger unit, such as gallons, is changed into a smaller one, such as quarts, you will have a greater number of units. If a smaller unit, such as inches, is changed into a larger unit, such as feet, you will have a smaller number of units. Write larger or smaller to show whether your answer will be a larger or smaller number of units. 1. changing ounces into pounds 2. changing yards into feet. changing gallons into quarts To change eight feet into inches, use the following steps. 4. Will the numeric portion of your answer be smaller or larger? Explain. 5. How many inches are in a foot? 6. How many feet are being changed into inches? Multiply the numbers in Exercises 5 and 6 together to get the number of inches in 8 feet. 7. How many inches are in 8 feet?
Puzzles, Twisters & Teasers Analyze This! Solve the crossword puzzle. Across 4. There are 1000 meters in a. 7. There are 12 in 1 foot. 8. There are 65 days in 1. 9. Ratios of equal quantities are called factors. 10. There are 4 quarts in 1. Down 1. Unit analysis is also called analysis. 2. There are 7 days in 1.. There are 60 in 1 minute. 5. There are 16 in 1 pound. 6. There are 100 centimeters in 1.
Answers LESSON 5- Practice A 1. larger 2. smaller. larger 4. 0.45 kg 5. 15,840 ft 6. 5 pints 7. 7.5 gallons 8. 224 oz 9. 1044 in. 10. 76 mm 11. about 5 miles 12. about 112 grams 1. about.8 Liters Practice B 1. 0. g 2. 1500 feet. 4.5 pints 4. 1.75 gallons 5. 296 oz 6. 2,900 mm 7. 22,500 g 8. about.5 Liters 9. about 9.4 inches 10. about 22.7 kilograms Practice C 1. 65 problems 2. 4216 cones..75 miles 4. 6 meals 5. 86,400 decals 6. 960 ft 6. 960 ft 7. 1,600,000 oz 8. 8007 oz 9. 7,920,000 body lengths Review for Mastery 1. 4 2. 100. 4. 12 in.; inches; 5. 16 oz; ounces; 1 ft 12 in. ; 6 1lb 16 oz ; 2.5 CODE 6. 100 cm; meters; 7. pounds; 1kg 2.2 lb ; 68.2 100 cm 1 m ; 7,500 60 mi 8. ; 1760; numerator; 1760 yd denominator; ; 105,600; 60; 1 mi denominator; numerator; 105,600; 1hr 60 min ; 1760 Challenge 1. 1 g 1 ml 1m 1 cm = 1 g 1 cm 2. 1,000,000 1 g. 1 cm 1kg 1000 g 1,000,000 cm 1 m 1000 kg 1 m 1000 kg 4. 1 m 8.5 lb 1 gal 5. 8.5 Problem Solving 2.205 lb 1 1m 264.2 gal 1. 8.7 mi 2. 14.9 miles an hour.,968. lb 4. 8.8 lb 5. 26.2 ft 6. 6.1ft 7. B 8. J 9. C 10. F Reading Strategies 1. smaller 2. larger. larger = =
4. The answer will be larger. You are changing from a larger unit of measure to a smaller one. 5. 12 6. 8 7. 96 inches Puzzles, Twisters & Teasers Across 4. KILOMETER, 9. CONVERSION, 10. GALLON, 7. INCHES, 8. YEAR Down 1. DIMENSIONAL, 5. OUNCES, 2. WEEK,. SECONDS, 6. METER