Length Conversions - Homeschool Giveaways

Length Conversions Many people are familiar with the U.S. Customary units of measure, either because they are using them now or have used them in the past. However, the metric system, while commonly used in many parts of the world, is not always as familiar to people in the United States. The metric system began as a result of the French National Assembly asking the French Academy of Sciences to try to standardize the system of weights and measures that had become so confused in France. In 1791, work on the new system was begun, and by 1795, all metric units had been set and identified in France. By 1799, the new units were declared the legal standards for every measurement used in France. In 1875, an international conference met in Paris to set up an International Bureau of Weights and Measures. Meetings are held to reconsider the way the units have been determined, and the system has been refined over the years. Today, the metric system, based on units of 10, has been officially adopted by most of the countries in the world. Below are two tables. The first shows the equivalency of 1 inch, 1 foot, 1 yard, and 1 mile to common metric measures. The second shows the equivalency of 1 millimeter, 1 centimeter, 1 meter, and 1 kilometer to common U.S. Customary measurements. For ease in use, we have rounded the measurements to two decimal places where possible. Millimeter

Centimeter

Meter

Kilometer

1 Inch

25.40

2.54

0.03

0.00003

1 Foot

304.80

30.48

0.30

0.0003

1 Yard

914.40

91.44

0.91

0.0009

1 Mile

1609344.00

160934.40

1609.34

1.61

Inch

Foot

Yard

Mile

1 Millimeter

0.04

0.003

0.001

---

1 Centimeter

0.39

0.03

0.01

0.000006

1 Meter

39.37

3.28

1.09

0.0006

1 Kilometer

39370.08

3280.84

1093.61

0.62

How do you convert between the two systems when the need arises? Use the standard methods of conversion shown in the tables above to solve the following practice problems.

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Activity One: If we know that 1 inch (in) = 25.4 millimeters (mm) or 2.54 centimeters (cm), find the answers to the following problems. 3 in. = __________ mm

3 in. = __________ cm

9 in. = __________ mm

7 in. = __________ cm

18 in. = __________ mm

20 in. = __________ cm

25 in. = __________ mm

23 in. = __________ cm

34 in. = __________ mm

36 in. = __________ cm

Activity Two: Now that you have your answers for the above problems, convert them into metric measurements. For example, we see that 3 in. equals 76.2 mm or 7.62 cm. There are 10 millimeters in a centimeter. To convert from millimeters to centimeters, you divide the number of millimeters by 10. To convert from centimeters to millimeters, you multiply the number of centimeters by 10. Using your answers in the exercise above, convert the millimeter answers to centimeters, and the centimeter answers to millimeters. The first one is done for you. 3 in. = 76.2 mm or 7.62 cm

3 in. = 7.62 cm or 76.2 mm

9 in. = _______ mm or _______cm

7 in. = _______ cm or _______mm

18 in. = _______ mm or _______cm

20 in. = _______ cm or _______mm

25 in. = _______ mm or _______cm

23 in. = _______ cm or _______mm

34 in. = _______ mm or _______cm

36 in. = _______ cm or _______mm


Activity Three: If we know that 1 cm equals .39 in., convert the following: 16 cm = __________ in.

77 cm = __________ in.

249 cm = __________ in.

94 cm = __________ in.

67 cm = __________ in.

152 cm = __________ in.

83 cm = __________ in.

194 cm = __________ in.

71 cm = __________ in.

239 cm = __________ in.

Activity Four: Using the fact that 1 foot (ft.) equals .30 meters (m) or 30.48 cm, find the answers to the following problems: 1. If you were building a room onto your house and you needed to make it 18 feet by 16 feet, what would those measurements be in meters? In centimeters?

2. If you bought a piece of property the measurements of which were 137 feet by 94 feet, what would those measurements be in meters? In centimeters?

3. If you were having a driveway paved that measured 12 feet by 20 feet and you had to give those measurements in meters, what would the measurements be? What would they be in centimeters?

4. Knowing there are 3 feet in a yard, how many meters of material would you need to buy if you were making something that required 6 yards of material?

5. For a race, you are making lines on the ground 15 feet apart so you can see who is in the lead at different points in the race. How many meters apart are the lines?


Activity Five: Now, using the fact that 1 m = 3.28 ft., compute the following: 16 m = __________ ft.

27 m = __________ ft.

23 m = __________ ft.

12 m = __________ ft.

35 m = __________ ft.

18 m = __________ ft.

52 m = __________ ft.

43 m = __________ ft.

30 m = __________ ft.

9 m = __________ ft.

Activity Six: Using the fact that 1 mile (mi.) equals 1.61 kilometers (km), do the following problems: 1. You are driving and see a sign that tells you your destination is 14 miles away. How many kilometers does that equal?

2. When figuring the distance to travel on your vacation, you find you will have to travel 175 miles. How many kilometers do you have to travel?

3. Your friend is coming to visit and tells you they have to make extra stops on the way, so they will be traveling a total of 83 miles. How many kilometers will they travel?

4. You have to total the distance traveled for reimbursement. You traveled 30 miles on Monday, 21 miles on Tuesday, 16 miles on Wednesday, and 9 miles on Thursday. How many total kilometers did you travel?

5. You need to determine the total distance to your grandmother’s house from your new home. Your grandmother lived 3 miles from your old home and you have moved 2 miles further away. How many kilometers do you now live from your grandmother’s house?


Activity Seven: Knowing that 1 km = .62 mi., do the following problems: 73 km = __________ mi.

94 km = __________ mi.

19 km = __________ mi.

42 km = __________ mi.

28 km = __________ mi.

61 km = __________ mi.

97 km = __________ mi.

32 km = __________ mi.

59 km = __________ mi.

17 km = __________ mi.


Answer Key: Activity One: 3 in. = 76.2 mm

3 in. = 7.62 cm

9 in. = 228.6 mm

7 in. = 17.78 cm

18 in. = 457.2 mm

20 in. = 50.8 cm

25 in. = 635 mm

23 in. = 58.42 cm

34 in. = 863.6 mm

36 in. = 91.44 cm

Activity Two: 3 in. = 76.2 mm or 7.62 cm

3 in. = 7.62 cm or 76.2 mm

9 in. = 228.6 mm or 22.86 cm

7 in. = 17.78 cm or 177.8 mm

18 in. = 457.2 mm or 45.72 cm

20 in. = 50.8 cm or 508 mm

25 in. = 635 mm or 63.5 cm

23 in. = 58.42 cm or 584.2 mm

34 in. = 863.6 mm or 86.36 cm

36 in. = 91.44 cm or 914.4 mm

Activity Three: 16 cm = 6.24 in.

77 cm = 30.03 in.

249 cm = 97.11 in.

94 cm = 36.66 in.

67 cm = 26.13 in.

152 cm = 59.28 in.

83 cm = 32.37 in.

194 cm = 75.66 in.

71 cm = 27.69 in.

239 cm = 93.21 in.

Activity Four: 1.

5.4 m by 4.8 m or 548.64 cm by 487.68 cm

2.

41.1 m by 28.2 m or 4175.76 cm by 2865.12 cm

3.

3.6 m by 6 m or 365.76 by 609.60 cm

4.

5.4 m

5.

4.5 m


Activity Five: 16 m = 52.48 ft.

27 m = 88.56 ft.

23 m = 75.44 ft.

12 m = 39.36 ft.

35 m = 114.8 ft.

18 m = 59.04 ft.

52 m = 170.56 ft.

43 m = 141.04 ft.

30 m = 98.4 ft.

9 m = 29.52 ft.

Activity Six: 1.

22.54 km

2.

281.75 km

3.

133.63 km

4.

122.36 km

5.

8.05 km

Activity Seven: 73 km = 45.26 mi.

94 km = 58.28 mi.

19 km = 11.78 mi.

42 km = 26.04 mi.

28 km = 17.36 mi.

61 km = 37.82 mi.

97 km = 60.14 mi.

32 km = 19.84 mi.

59 km = 36.58 mi.

17 km = 10.54 mi.
