English Measurement Relationships

Transcription

1 Math 20 Arithmetic Sec 7.1: Problem Solving with English Measurement In the U.S., we use the English system of measurement for many everyday activities. Examples of English units are inches, feet, quarts, ounces, and pounds. However, the fields of science, medicine, sports, and manufacturing use the metric system (meters, liters, and grams). Because the rest of the world uses only the metric system, the U.S. businesses have been shifting to the metric system in order to compete internationally. English Measurement Relationships Length Weight 1 foot (ft) = 12 inches (in) 1 pound (lb) = 16 ounces (oz) 1 yard (yd) = 3 feet (ft) 1 ton (T) = 2000 pounds (lb) 1 mile (mi) = 5280 feet (ft) Capacity Time 1 cup (c) = 8 fluid ounces (fl oz) 1 minute (min) = 60 seconds (sec) 1 pint (pt) = 2 cups (c) 1 hour (hr) = 60 minutes (min) 1 quart (qt) = 2 pints (pt) 1 day = 24 hours (hr) 1 gallon (gal) = 4 quarts (qt) 1 week (wk) = 7 days Converting Among Measurement Units 1) Multiply when converting from a unit to a unit. ex 2) Divide when converting from a unit to a unit. Ex 1 Convert each measurement using unit fractions. a) b) c) (#16) A reticulated python snake is the world's longest snake. It grows to the length of 18 feet to 33 feet. How many yards long can the snake be? d) e) Page 1 of 12

2 f) g) Ex 2 Convert each measurement. You may be required to use more than one unit fraction. a) b) c) d) e) f) g) Page 2 of 12

3 Ex 3 (#56) Zach paid $0.79 for a 1.6 oz candy bar. What was the cost per pound? Convert first? Ex 4 (#60) A snail moves at an average speed of 2 feet every 3 minutes. At that rate, how long would it take the snail to travel one mile? Sec 7.2: The Metric System -- Length The metric system is based on multiples of 10, like our number system and our money. The basic unit of length of the metric system is the meter. To make longer and shorter length units in the metric system, we use prefixes in front of the word meter. The shaded boxes are the units you will use most often in daily life. Move LEFT Move RIGHT Prefix Meaning kilometer 1000 meters hectometer 100 meters Symbol km hm dekameter 10 meters dam or Dm meter 1 meter decimeter of a meter centimeter of a meter millimeter of a meter m dm cm mm Metric Length Relationships Unit Fractions: Unit Fractions: Unit Fractions: Unit Fractions: Ex 5 Write the most reasonable metric length unit in each blank. a) The cardboard was 3 thick. b) The bookcase is 75 wide. c) The door is 2 high. d) Lamard jogs 4 every morning. e) My pen is 145 long. f) Wheelchairs need doorways that are at least 80 wide. Page 3 of 12

4 Ex 6 Convert each measurement. Use unit fractions OR the metric conversion line. a) b) c) d) e) f) g) h) i) Ex 7 (#38) Is 1022 m greater than or less than 1 km? What is the difference in lengths? Sec 7.3: The Metric System -- Capacity and Weight (Mass) The basic unit for capacity is liter and the symbol for liter is L. A box that measures 10 cm on every side holds exactly one liter. A liter is just a little more than a quart (just cup more). Page 4 of 12

5 The gram is the basic metric unit for mass. Although we often call it "weight," there is a difference. Weight is the measure of pull of gravity, the farther you are from the center of Earth, the less you weigh. In outer space you become weightless, but your mass, the amount of matter in your body remains the same, regardless of where you are. Ex 8 Write the most reasonable metric unit in each blank. Choose from and. a) Hiromi used 12 of water to wash the kitchen floor. b) Jay gave 2 of vitamin drops to the baby. c) One dime weighs 2. d) Barbara bought the 2 bottle of cola. e) The 8 people on the elevator weighed a total of 500. f) Kevin poured 10 of vanilla into the mixing bowl. g) One grain of sea salt weighs 2. Ex 9 Convert each measurement. Use unit fractions OR the metric conversion line. a) b) c) d) e) f) g) h) i) Page 5 of 12

6 j) k) Ex 10 (#66) A healthy human heart pumps about 70 ml of blood per beat. How many liters of blood does it pump per beat? Ex 11 (#74) The ratio of the total length of all the fish to the amount of water in an aquarium can be 3 cm of fish for every 4 L of water. What is the total length of all fish you can put in a 40 L aquarium? Ex 12 You are serving a 40-kg turkey for 28 people. How many grams of meat is each person allowed? Write final answer as a mixed number. Sec 7.4: Problem Solving with Metric Measurement Ex 13 (#2) Lanh is buying a piece of plastic tubing measuring 3 m 15 cm for the science lab. The price is $4.75 per meter. How much will Lanh pay? $14.96 (rounded) Page 6 of 12

7 Ex 14 (#8) The apartment building caretaker puts 750 ml of chlorine into the swimming pool every day. How many liters should he order to have a one-month (30-day) supply on hand? If chlorine is sold in containers that hold 4 L, how many containers should be ordered for one month? How much chlorine will be left over at the end of the month? 22.5 L; 6 containers; 1.5 L left over Ex 15 (#14) Lorenzo's doctor has suggested that he cut down on caffeine, so Lorenzo switched from drinking four 8-oz cups of cola every day to drinking two 8-oz cups of decaffeinated coffee. How much fewer grams of caffeine is he consuming each week? Sec 7.5: Metric-English Conversions and Temperature Page 7 of 12

8 Note: As altitude increases (at higher altitudes), air pressure decreases. As a result, so does the boiling point. Ex 16 Use the table to make approximate conversions. Round to the nearest hundredth when necessary. a) 8 km to mi b) 85 cm to in c) 3.2 yd to m d) 2.5 oz to g e) 7.68 kg to lb (calc) f) L to gal (calc) lb 4.10 gal Page 8 of 12

9 Ex 17 (#16) The rinse-and-hold cycle in a dishwasher uses only 4.5 L of water. How many gallons does it use, to the nearest tenth? Ex 18 (#18) The fastest nerve signals in the human body travel 120 m per second. How many feet per second do the signals travel? Ex 19 Convert to Celsius or Fahrenheit degrees. Provide both the exact and rounded (to the nearest degree) answer. a) b) c) Ex 20 (#38) Sleeping bags made by Eddie Bauer are sold around the world. Each type of sleeping bag is designed for outdoor camping in certain temperatures. Junior Bag or warmer a) At what Fahrenheit temperatures should you use the Junior bag? Removable Liner Bag to Conversion Bag to b) What Fahrenheit temperatures is the removable liner bag designed for? Page 9 of 12

10 Ex 21 Convert. Do not round! a) 4 oz to T b) 5 gal to c c) 8 inches to ft Ex 22 (CT #23*) The rainiest place in the world is Mount Waialeale in Hawaii, which receives 460 inches of rain each year. What is the average rainfall per month, in feet? Provide the exact answer. Next, round to the nearest tenth. REVIEW: Convert each to a fraction or mixed number. Page 10 of 12

11 Review: Sec 8.8: Pythagorean Theorem List perfect squares. Know these perfect squares for test. Defn The square root of a number is the number where and. In symbols,, if. - indicates square root and is called a radical sign Note: The result upon taking the square root is always nonnegative. Ex 23 Simplify. (Find the square root and simplify.) a) b) c) d) e) f) Challenge :) ( ) Pythagorean Theorem In any right triangle, if is the length of the hypotenuse and and are the lengths of the two legs, then. Page 11 of 12

12 Ex 24 Find the unknown length of each triangle. 9 cm 9 cm 12 cm 16 cm Ex 25 William drove his car 15 miles north, then made a right turn and drove 7 miles east. How far is he from his starting point? Draw a sketch to illustrate the problem and solve it. Page 12 of 12