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 m. How many m 2 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 paint. Each liter of paint covers 13 m 2 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 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 (FIN) 2:20.8 1960 (NOR) and Yevgeny Grishin (URS) 2:10.4 1980 (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

4. 750 m2 19. 37.4 °C

5. 55 m2 20. 50g

6. 1600 cm3 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

12. -22c 27. 600ml

13. 2000cm2 28. 30 kg

14. 1m 29. 49 c

15. 9.85sec 30. 1 kW

31. 6t

32. a. 3200000cm3 b. 4900000mm2 c. 500mm2 d. 6 cm 2

33. 1.2 m3

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). A picosecond is 1000 times smaller than a nanosecond, therefore it takes 5280 x 1000 = 5,280,000 picoseconds for light to travel a mile.

46. Citius, Altius, Fortius The answer would be Yevgeny Grishin and Roald Aas, Eric Heiden, Aadne Sondraal, Annie Borckink, and Marianne Timmer.

This is actually very easy when you figure out how to do it. The question is, basically, who runs faster than 25 miles per hour. The speed is measured by how long it takes for them to run/skate through a 1500-meter field.

Meters (1,500-meter dash) and miles (25 mph) are in two different systems though, and it would be almost impossible to work with that, so we would have to convert 25 mph to kilometers.

Kilometer is the closest to a mile in the metric system. I did some research and found that there were 0.6214 kilometers in a mile.

Now we divide 25 (mph) by 0.6214 to find the kilometers in 25 mph. That equals 40.23 kilometers per hour. That means in 1 hour, they must travel 40.23 km or more. 1 hour equals 60 minutes. 1500 meters equals 1.5 kilometers. There are 1000 meters in a kilometer. If 40.23 kilometers takes up 60 minutes, what would it take them to run 1.5 kilometers (which is the distance they must run)? Here's the equation. 40.23 km = 60 minutes. 1.5 km = X.

In a case like this, you would use algebra. We would cross-multiply. To cross-multiply, you multiply one side of the equation with the other side of the other equation. So 1.5 times 60 equals 40.23 times X. Now we need to find out what X is.

1.5 time 60 equals 90. Now to find X, you would divide it by 40.23. We do this because the quotient times the divisor is the dividend (for example, 6/3=2 and 2x3=6). 90 divided by 40.23 equals 2.24 minutes.

We know that 1 minute equals 60 seconds. Let’s take the 2 minutes out for now (to make it easier) and find the seconds in 0.24 minutes. This 24 is out of 100 when in the time system, it should be out of 60 (there are 60 second in a minute, not 100).

So 0.24 times 60 (the number of seconds in a minute) equal 14.4 seconds. Now we add the two minutes we took out back. It would come to 2 minutes, 14 seconds, and 4 hundredths of a second. That is how fast a runner must be to run at 25 mph. If it takes him/her more than that, he/she didn’t go faster than 25 mph.

Conclusion Looking at the runners times, the people who exceeded the limit are Roald Aas and Yevgeny Grishin, Eric Heiden, Aadne Sondraal, Annie Borckink, and Marianne Timmer. Nobody in the running group exceeded 25 mph.

BONUS

Bonus: The first step I took was to change all the values into tenths of a second. To do this I multiplied the minutes by 600 and the seconds by 10. Then I added these up and and added the tenths of a second. These are the values I got for each person:

Clas Thunberg - 1408 Roald Aas, Yevgeny Grishin - 1304 Eric Heiden - 1154.4 Aadne Sondraal - 1078.7

Lydia Skoblikova - 1452 Annie Borckink - 1309.5 Marianne Timmer - 1175.8

Paavo Numri - 2326 Herbert Elliott - 2156 Steve Ovett - 2121 Hicham El Guerrouj - 2060 Anna Muskina - 3182 Diane Leather - 2697 Tatyana Kazankina - 2350 Qi Uunixa - 2304.6

Knowing these values, I subtracted the time of the skater from the time of the runner. Then I made a proportion for each one:

1500 x ------= ------time of runner time left after skater finishes

This way, when I found x, I would have how many more meters the runner has to travel after the skater finishes, therefore finding out how far behind the runner is.

I got the following results:

1924 men - 592 m 1960 men - 593m 1980 men - 684m 1998 men - 715m 1960 women - 692m 1980 women - 664m 1998 women - 735m

47. Baseball Trivia The Phillies need to score 15 runs before the base runners have covered a mile.

The first thing I needed to know is the distance between each base. I know that the distance between each base is 90 feet in Major League Baseball. Then I figured out the amount of feet in a mile, which is 5,280 feet. Since a baseball field is the shape of a diamond, I figured out the distance for one runner to travel around all four bases, which is 4x90feet= 360feet. To find the total number of runs the Phillies had to score I divided 5,280feet by 360feet per run to get how many runs were needed. When divided, this equals 14.67 runs. Since you can't have a partial run in baseball I rounded this number up to 15 runs. In other words the Phillies need to score 15 runs to cover a mile.

Bibliography Information

Teachers attempted to cite the sources for the problems included in this problem set. In some cases, sources may not have been known.

Problems Bibliography Information

Barton, David. Alpha Mathematics. Auckland: 32-38 (mixture) Longman.

Barton, David. Alpha Mathematics Homework 32-38 (mixture) Book. Longman. ISBN 0 582 54260 X. Pearson Education New Zealand, 2000.

Barton, David. Beta Mathematics. Pearson 32-38 (mixture) Education New Zealand.

Barton, David. Beta Mathematics Homework Book. ISBN 978-1-4425-0017-4. Pearson 32-38 (mixture) Education New Zealand, 2000.

Barton, David. Gamma Mathematics 1-31 Pearson Education. New Zealand, 2000

Zaccaro, Edward. Challenge Math (Second 43-45 Edition): Hickory Grove Press, 2005.

The Math Forum @ Drexel 46-47 (http://mathforum.org/)