Chapter 7: Measurement

1. Chapter 7: Measurement

2. 7.1 Converting U.S. Customary Units of Length

3. U.S. Customary Units of Length • To measure an object means to assign it a number and a unit of measure. • One common system of units is the U.S. Customary System of measurement.

4. Converting U.S. Customary Units of Length by Using Substitution Example: 4 ft = ____ in. Solution:

5. Converting U.S. Customary Units of Length by Using Unit Ratios • A conversion factor is a ratio of equivalent measures. • These ratios are called unit ratios (or unit fractions).

6. Converting U.S. Customary Units of Length by Using Unit Ratios Example: 9240 yd = ___ mi Solution:

7. Adding and Subtracting Mixed Units Example: Add 4’6” + 2’9”. Solution:

8. Adding and Subtracting Mixed Units Example: Subtract 8’2” – 3’6”. Solution:

9. Applications Example: Solution:

10. Applications Example: A carpenter has a board 6’10” in length. He must cut the board into two pieces of equal length. How long is each piece? Solution:

11. Exercise 1 Convert the units of length by using a unit ratio. A). 21 ft B). 8 ft C). 6.3 ft D). 7 ft

12. Exercise 2 Subtract as indicated. 9’2” – 4’10” A). 4’2” B). 4’4” C). 5’4” D). 4’6”

13. Exercise 3 A picnic table requires 5 boards that are 6’ long, 4 boards that are 3’3” long, and 2 boards that are 18” long. Find the total length of lumber required. A). 46’ B). 47’4” C). 45’6” D). 45’

14. 7.2 Converting U.S. Customary Units of Time, Weight, and Capacity

15. U.S. Customary Units of Time, Weight, and Capacity

16. Converting U.S. Customary Units of Time Example: 36 hr = _____ sec Solution:

17. Converting U.S. Customary Units of Weight Example: The average weight of an adult male African elephant is 12,400 lb. Convert this value to tons. Solution:

18. Applying U.S. Customary Units of Weight Example: Jessica lifts four boxes of books. The boxes have the following weights: 16 lb 4 oz, 18 lb 8 oz, 12 lb 5 oz, 22 lb 9 oz. How much weight did she lift altogether?

19. Applying U.S. Customary Units of Weight Solution:

20. Converting Units of Capacity Example: 1.25 pt = ___ qt Solution:

21. Applying Units of Capacity Example: A recipe calls for 1 ¾ c of chicken broth. A can of chicken broth holds 14.5 fl oz. Is there enough chicken broth in the can for the recipe? Solution: The can of chicken broth holds 14.5 fl oz which is enough.

22. Exercise 4 Convert the units of time. 168 hr = ___ wk A). 1.1 B). 0.9 C). 1 D). 1.5

23. Exercise 5 Convert the units of weight. A). 6000 B). 6500 C). 7000 D). 6750

24. Exercise 6 A box that contains 6 identical textbooks weighs 15 lb 12 oz. What is the weight of each textbook? A). 2 lb 9 oz B). 2 lb 8 oz C). 3 lb 2 oz D). 2 lb 10 oz

25. 7.3 Metric Units of Length

26. Introduction to the Metric System • The metric system is the predominant system of measurement used in science. • The base units are the meter for length, the gram for mass, and the liter for capacity. • Other units in the metric system are multiples of 10 of the base units.

27. Metric Units of Length • The meter (m) is the basic unit of length in the metric system. • The meter is slightly longer than a yard.

28. Metric Units of Length

29. Measuring Distances in Metric Example: Approximate the distance in centimeters and in millimeters. Solution: The length of the screw appears to be approximately 5 cm or 50 mm.

30. Converting Metric Units of Length Example: 10.4 km = _____ m Solution:

31. Converting Metric Units of Length by Using the Prefix Line • Since the metric system is based on powers of 10, we can convert between two metric units by moving the decimal point. • The direction and number of place positions to move are based on the metric prefix line.

32. Converting Metric Units of Length by Using the Prefix Line

33. Converting Metric Units of Length by Using the Prefix Line Example: 4700 cm = ____ m Solution:

34. Exercise 7 Approximate the distance in centimeters. A). 2.7 cm B).2.5 cm C). 27 cm D). 2.9 cm

35. Exercise 8 Convert the metric units of length using the prefix line. 450 mm = ____ dm A). 0.45 dm B). 4.5 dm C). 0.045 dm D). 45 dm

36. Exercise 9 The Trump World Tower in Atlanta is 269 m tall. How many kilometers is this? A). 269,000 km B). 2.69 km C). 0.0269 km D). 0.269 km

37. 7.4 Metric Units of Mass and Capacity

38. Metric Units of Mass • The fundamental unit of mass in the metric system is the gram (g).

39. Metric Units of Mass

40. Converting Metric Units of Mass Example: 1400 mg = ____ g Solution:

41. Converting Metric Units of Mass Solution:

42. Metric Units of Capacity • The basic unit of capacity in the metric system is the liter (L). 1 mL is equivalent to a cubic centimeter (cc or cm3).

43. Converting Metric Units of Capacity Example: 150 cL = ____ kL

44. Converting Metric Units of Capacity Solution:

45. Summary of Metric Conversions Example: The mass of a bag of rice is 90,700 cg. Convert this to grams. Solution:

46. Exercise 10 Convert the units of mass. 0.003 kg = ____ dg A). 3 B). 30 C). 0.3 D). 300

47. Exercise 11 Convert the units of capacity. 0.88 L = ____ hL A). 0.0088 B). 88 C). 0.088 D). 0.00088

48. Exercise 12 A gasoline can has a capacity of 19 L. Convert this to kiloliters. A). 0.0019 B). 19,000 C). 0.19 D). 0.019

49. 7.5 Converting Between U.S. Customary and Metric Units

50. Summary of U.S. Customary and Metric Unit Equivalents Example: Use the fact that 1 mi  1.61 km to convert 45 km to miles. Round to the nearest mile.