Black – Decimals Place Value Measure Decimals Unit 3 Lesson 1: Metric Conversions Complete each real-life example by inserting the correct measurement from the list on the right. Use the table on the next page for guidance. 1. A teaspoon holds ____ 0.5 ha 2. The average person has about ____ of blood. 1 kg 3. Mt Cook is ____ high. 1 m 4. A typical urban section is ____ in area. 1 kW 5. A classroom is about ____ in area. 100 km/h 6. The engine capacity for a Toyota Corolla is ____ 1500 m 7. The power rating of a light-bulb is ____ 160 kPa 8. The height of a doorway is ____ 1600 cm³ 9. Pepsi is sold in ____ bottles. 180 mm 10. A average-sized man weighs about ____ -22ºC 11. A car petrol tank holds about ____ 2 m 12. The coldest temperature recorded in New Zealand is ____ 2 L 13. The area of a school desk is ____ 200 ml 14. A long stride when walking is about ____ 2000 cm² 15. The world record for the 100 meters sprint is ____ 30 kg 16. This book weighs about ____ 37.4ºC 17. The metric equivalent of a mile is ____ 3760 m 18. A typical pressure for car tires is ____ 40 L 19. The temperature of a healthy human being is ____ 49ºC 20. An onion weighs about ____ 5ml 21. The length of a pencil is ____ 50 g 22. The speed limit on the open road is ____ 500 g 23. A packet of butter weighs ____ 55 m² 24. A plastic container of ice-cream contains ____ 6 t 25. Milk is sold in cartons that each hold ____ 60 W 26. A hockey field has an area of approximately ____ 600 ml 27. A tea cup holds about ____ 750 ml 28. A heavy suitcase weighs about ____ 750 m² 29. The hottest temperature ever recorded was ____. 8 L 30. A fan-heater has a power consumption of ____ 80 kg 31. A fully loaded shipping container weighs ____ 9.85 s Abbreviations Volume Volume cm³ = centimeter cubed or 1 000 000 cm³ = 1 m³ cubic centimeter m³ = meter cubed Area Area 1 hectare = 10 000m2 ha =hectare Mass Mass mg = milligram 1000 mg = 1 g g = gram 1000 g = 1 kg kg = kilogram 1000 kg = 1 tonne Capacity Capacity ml = milliliter 1 ml = 1 cm³ L = liter 1000 ml = 1 liter Pressure Kpa = Kilopascal Electric Power kW = kilowatt W = watt Convert to the unit indicated 32. a. 3.2 m³ = ………. (cm³) b. 4.9 m²to mm². c. 5 cm²to mm². d. 600 mm²to cm². 33. 1 200 000 cm²= ………. (m³) 34. A liter container of juice must have an internal volume of how many cubic centimeters? 35. If the average weight of students is 46 kg find the weight (in tons) of a bus load of 31 students? 36. A cubic meter of soil weighs 1400 kg. How many tons will the soil from a bank weigh in tons, if the bank’s volume is 3.4 m by 2 m by 1.5 m? 37. Application Problem. 3.2 tons of topsoil is to be spread over a new section. The section is 32 m by 27.6 m, how many kilograms of topsoil should be spread on each square meter? 38. Problem Solving. A box of 100 biscuits originally weighs 1.325 kg. 55 biscuits are eaten and the remaining biscuits and box now weigh 637.6 g, how much does the box weigh? Solve the following problems. 39. A driveway is to be paved. It is 26 m long and 5 m wide. The cost of the pavers is $23.50 per m 2 and $14 per m 2 for laying. What is the total cost of paving the driveway? 40. A rectangular swimming pool is 15 m long, 4.5 m wide and 1.4 m deep. a. Find the volume of the swimming pool. b. How many liters of water would the pool hold (1 m 3 = 1000 L)? c. If the pool can be filled at the rate of 35 liters/min how long would it take (hours and minutes) to fill the pool? 41. A cylindrical water tank is to be made and has a radius of 1.3 m and the height of 2 2 m. How many m of sheet metal will be required to make the water tank? 42. The exterior of a barn is to be painted (including the flat roof) with two coats of 2 paint. Each liter of paint covers 13 m and costs $15.70 per liter. a. Calculate the area to be painted. b. How many liters of paint will be required for two coats? c. What is the cost of painting the barn? Use the following information to answer questions 43-45. A microsecond is a millionth of a second → .000001 A nanosecond is a billionth of a second → .000,000,001 A picosecond is a trillionth of a second → .000,000,000,001 A femosecond is a quadrillionth. → of a second. .000,000,000,000,001 43. Light travels approximately one foot in a nanosecond. How far does light travel in a microsecond? 44. 372 picoseconds equal _________ femoseconds? 45. How many picoseconds does it take for light to travel a mile? 46. Citius, Altius, Fortius The Olympic motto is "Citius, Altius, Fortius." These three Latin words mean "Swifter, Higher, Stronger." Speed skaters sure follow the Olympic motto! Men's speed skating was an event in the first Winter Games in 1924. Women's speed skating became an event for the first time during the 1960 Games. Here are some Gold Medal times for the 1500-meter speed skating event: NOTE: All times are expressed in minutes : seconds . hundredths of a second. MEN'S 1924 Clas Thunberg (FIN) 2:20.8 1960 Roald Aas (NOR) and Yevgeny Grishin (URS) 2:10.4 1980 Eric Heiden (USA) 1:55.44 1998 Aadne Sondraal (NOR) 1:47.87 WOMEN'S 1924-1956 Event not held 1960 Lydia Skoblikova (URS) 2:25.2 1980 Annie Borckink (NED) 2:10.95 1998 Marianne Timmer (NED) 1:57.58 Unlike speed skaters, who skate against the clock, distance runners in the 1500- meter races of the Summer Olympics compete in a group. They have to beat the athletes they're running against, which may lead to a different mindset than trying for the best possible time. A World Record, however, is a good measure of the fastest 1500-meter race on foot, so let's look at some of those results: NOTE: The earliest World Records for women are from 1927. MEN'S 1924 Paavo Nurmi (FIN) 3:52.6 1960 Herbert Elliott (AUS) 3:35.6 1980 Steve Ovett (GBR) 3:32.1 1998 Hicham El Guerrouj (MOR) 3:26.00 WOMEN'S 1927 Anna Muskina (URS) 5:18.2 1960 Diane Leather (GBR) 4:29.7 1980 Tatyana Kazankina (URS) 3:55.0 1998 Qu Yunxia (CHN) 3:50.46 Now imagine that these Olympians and World Record holders are skating or running in a residential area at their record speeds. Who might be arrested for excessive speed in that residential zone if the posted speed limit is 25 miles per hour? BONUS Let's imagine the speed skater and runner from each year starting a race side by side. How far behind is each runner when the skater crosses the finish line? 47. Baseball Trivia The Phillies are a baseball team that plays in Philadephia, Pennsylvania. The game of baseball provides many opportunities to use math skills. To score a run in baseball, a runner has to run around all the bases, starting at home plate, in a diamond shape. There are 90 feet in between each base. How many runs do the Phillies have to score before the scoring base runners have covered a mile? Solutions - Black – Decimals Place Value Measure Decimals Unit 3 Lesson 1 Metric Conversions 1. 5 ml 16. 1kg 2. 8 L 17. 1500m 3. 3760 m 18. 160kPa 2 4. 750 m 19. 37.4 °C 2 5. 55 m 20. 50g 3 6. 1600 cm 21. 180mm 7. 60 W 22. 100km/h 8. 2 m 23. 500g 9. 750 ml 24. 2L 10. 80kg 25. 200ml 11. 40L 26. 0.5 ha c 12. -22 27. 600ml 2 13. 2000cm 28. 30 kg c 14. 1m 29. 49 15. 9.85sec 30. 1 kW 31. 6t 3 32. a. 3200000cm 2 b. 4900000mm 2 c. 500mm 2 d. 6 cm 3 33. 1.2 m 34. 1000 cubic centimeters 35. 1426 kg = 1.426 tons 36. 14.28 tons 37. 3.6 kg per square meter 38. The box weighs 75 g and each biscuit weighs about 12.5 g 39. $4875 40. a. 94.5 m3 b. 94500 L c. 2700min or 45 hours 41. 26.94 m² 42. a. 392.28 m2 b. 30.175 L (3 decimal points) c. $473 43. 1000 feet A millionth of a second is 1000 times longer than a billionth of a second. Therefore light travels 1000 feet in a microsecond. 44. 372,000 femoseconds A femosecond is 1000 times smaller than a picosecond. In one picosecond there are 1000 femoseconds. There are 372 x 1000 = 372,000 femoseconds in 372 picoseconds. 45. 5,280,000 picoseconds Because light travels one foot in a nanosecond, it takes 5280 nanoseconds for light to travel a mile (5280 feet).