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## Chapter 7: Measurement

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**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.**Converting U.S. Customary Units of Length by Using**Substitution Example: 4 ft = ____ in. Solution:**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).**Converting U.S. Customary Units of Length by Using Unit**Ratios Example: 9240 yd = ___ mi Solution:**Adding and Subtracting Mixed Units**Example: Add 4’6” + 2’9”. Solution:**Adding and Subtracting Mixed Units**Example: Subtract 8’2” – 3’6”. Solution:**Applications**Example: Solution:**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:**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**Exercise 2**Subtract as indicated. 9’2” – 4’10” A). 4’2” B). 4’4” C). 5’4” D). 4’6”**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’**7.2 Converting U.S. Customary Units of Time, Weight, and**Capacity**Converting U.S. Customary Units of Time**Example: 36 hr = _____ sec Solution:**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:**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?**Applying U.S. Customary Units of Weight**Solution:**Converting Units of Capacity**Example: 1.25 pt = ___ qt Solution:**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.**Exercise 4**Convert the units of time. 168 hr = ___ wk A). 1.1 B). 0.9 C). 1 D). 1.5**Exercise 5**Convert the units of weight. A). 6000 B). 6500 C). 7000 D). 6750**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**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.**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.**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.**Converting Metric Units of Length**Example: 10.4 km = _____ m Solution:**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.**Converting Metric Units of Length by Using the Prefix Line**Example: 4700 cm = ____ m Solution:**Exercise 7**Approximate the distance in centimeters. A). 2.7 cm B).2.5 cm C). 27 cm D). 2.9 cm**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**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**Metric Units of Mass**• The fundamental unit of mass in the metric system is the gram (g).**Converting Metric Units of Mass**Example: 1400 mg = ____ g Solution:**Converting Metric Units of Mass**Solution:**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).**Converting Metric Units of Capacity**Example: 150 cL = ____ kL**Converting Metric Units of Capacity**Solution:**Summary of Metric Conversions**Example: The mass of a bag of rice is 90,700 cg. Convert this to grams. Solution:**Exercise 10**Convert the units of mass. 0.003 kg = ____ dg A). 3 B). 30 C). 0.3 D). 300**Exercise 11**Convert the units of capacity. 0.88 L = ____ hL A). 0.0088 B). 88 C). 0.088 D). 0.00088**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**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.