6.5 Metric U.S. Customary Measurement Conversions

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1 6. Metric U.S. Customary Measurement Conversions Since most of the world uses the metric system of measurement, we often need to know how to convert back and forth between U.S. Customary measurements and metric measurements. The good news is that we can use unit fractions using the relationships in the tables below! (It is also useful to have some of these relationships memorized so you can make sense of the units just in case you find yourself traveling outside of the U.S.) U.S. Customary to Metric Length in. = 2.4 cm ft 0.30 m yd 0. m mi.6 km Mass (Weight) oz 28.3 g lb 0.4 kg Volume (Capacity) fl oz 0.03 L pt 0.47 L qt 0. L gal 3.7 L Metric to U.S. Customary Length cm 0.3 in. m 3.28 ft m.0 yd km 0.62 mi Mass (Weight) g 0.03 oz kg 2.20 lbs Volume (Capacity) L fl oz L 2.0 pt L.06 qt L 0.26 gal Example : Use unit fractions to convert 8.3 meters to yards. Round your answer to the nearest tenth if necessary. 8.3 m 8.3 m.0 yd m Write down what is given over denominator. There is a direct relationship between meters and yards: m.0 yd m.0 yd We have two choices for the unit fraction, or.0 yd m. Choose.0 yd since the denominator has the unit we want to cancel. m Write the unit fraction to the right of what is given and divide out units yd Notice we are left with the units that the problem is asking for.

2 8.3.0 yd Multiply the numerators. Multiply the denominators..047 yd Divide the numerator by the denominator..047 yd Round to the nearest tenth..0 yd So 8.3 m.0 yd. Note: We could have also used the relationship from the U.S. Customary to Metric table: yd 0. m 8.3 m yd 0. m 8.3 yd yd yd Round to the nearest tenth..2 yd Notice that the answer is slightly different from the.0 yd above! This is because the values in both of the tables are rounded. So which relationship is better? m.0 yd or yd 0. m? In this course both relationships are fine to use, however, you may want to consider a few things: ) Your instructor (or perhaps boss) will often indicate which one they prefer you to use. Make sure you follow their instructions. 2) Some students prefer using m.0 yd since they don t have to divide. (This is helpful if you ever find yourself without a calculator where it may be more difficult to divide decimal numbers than to multiply them.) 3) Sometimes only one of the relationships is given so you don t have to worry about choosing the one that gives you the quickest computation. You Try It : Use unit fractions to perform the following conversions. Round your answers to the nearest tenth if necessary. a) 23 m to yds b) 40 cm to in. c) mi to km 2

3 Example 2: Use unit fractions to convert 36 pounds to kilograms. Round your answer to the nearest tenth if necessary. 36 lbs Write down what is given over denominator. There is a direct relationship between lbs and kg: kg 2.2 lbs 36 lbs kg 2.2 lbs 36 kg kg 2.2 We have two choices for the unit fraction, Choose kg 2.2 lbs kg 2.2 lbs or 2.2 lbs kg. since the denominator has the unit we want to cancel. Write the unit fraction to the right of what is given and divide out units. Notice we are left with the units that the problem is asking for. Multiply the numerators. Multiply the denominators kg Divide the numerator by the denominator. 6.8 kg Round to the nearest tenth. 6.8 kg So 36 lbs 6.8 kg. Note: We could have also used the relationship from the U.S. Customary to Metric table: lb 0.4 kg We would have obtained 36 lbs 6.2 kg, a slightly different answer. You Try It 2: Use unit fractions to perform the following conversions. Round your answers to the nearest tenth if necessary. a) 240 lbs to kg b) 3. kg to lbs c) 8 oz to g 3

4 Example 3: Use unit fractions to convert 8.2 gal to liters. Round your answer to the nearest tenth if necessary. 8.2 gal 8.2 gal 3.7 L gal L L Write down what is given over denominator. There is a direct relationship between gallons and liters: gal 3.7 L We have two choices for the unit fraction, gal or 3.7 L. 3.7 L gal Choose 3.7 L since the denominator has the unit we want to cancel. gal Write the unit fraction to the right of what is given and divide out units. Notice we are left with the units that the problem is asking for. Multiply the numerators. Multiply the denominators L Divide the numerator by the denominator L Round to the nearest tenth. 6.0 L So 8.2 gal 6.0 L. Note: We could have also used the relationship from the U.S. Customary to Metric table: L 0.26 gal We would have obtained 8.2 gal = 70 L, a slightly different answer. You Try It 3: Use unit fractions to perform the following conversions. Round your answers to the nearest tenth if necessary. a) 3. gal to L b) L to qts c).8 pts to L 4

5 Example 4: Use unit fractions to convert 4.7 kilograms to ounces. Round your answer to the nearest tenth if necessary. Write down what is given over denominator. 4.7 kg There is no direct relationship between kilograms and ounces! Write down any relationships from the tables involving kilograms and ounces: g 0.03 oz kg 2.20 lbs oz 28.3 g lb 0.4 kg Figure out a path to get from kilograms to ounces: kilograms grams ounces Notice that we can use what we know from Section 6.4 to convert kilograms to grams! We use the direct relationship kg = 000 grams to set up a unit fraction to take care of the conversion all at one time. Choose the appropriate unit fractions and write them in order to the right of what is given. First choose 000 g kg Then choose oz 28.3 g since we want to cancel out kilograms and be left with grams. since we want to cancel out grams and be left with ounces. 4.7 kg 000 g oz kg 28.3 g Now divide out units to make sure you will be left with ounces in the final answer. 4.7 kg 000 g kg oz 28.3 g oz 28.3 Multiply the numerators. Multiply the denominators oz 28.3

6 oz Divide the numerator by the denominator. Round to the nearest tenth oz 6.8 oz Note: We could have also taken a slightly different path to get to ounces: kilograms pounds ounces kg 2.2 lbs and lb = 6 oz (from the U.S. Customary relationships insection 6.3) Does it really matter which path we take? 4.7 kg 2.2 lbs 6 oz kg lb oz 6.44 oz 6.44 oz Round to the nearest tenth. 6.4 oz (a slightly different answer from 6.8 oz above) In this course it really should not be an issue as long as you are showing the correct unit fraction set-up to convert from the given units to the units the problem is asking for. We always recommend asking your instructor or a tutor to check your work for a few of these types of homework problems so they can provide the proper feedback to you. You Try It 4: Use unit fractions to convert.3 kilograms to ounces. Round your answer to the nearest tenth if necessary. 6

7 Once we are comfortable with choosing the appropriate unit fractions to convert back and forth between U.S. Customary and metric units, we can combine what we have learned from Sections 6.3, 6.4, and this section to answer the following types of problems. Example : The price of milk is $3.37 per gallon. Find the price per liter. Rewrite each per statement: $3.37 per gallon = $3.37 gal price per liter = price ($) L Now we can see that the problem wants us to convert $3.37 gal to price ($) L. Notice that there are two types of units involved: money and capacity Both monies are already in dollars so we only need to perform one conversion: gallons Choose the appropriate unit fraction and attach it to the right of what is given. Attach gal 3.7 L to convert gallons to liters. $3.37 gal gal 3.7 L liters Now divide out units to make sure you will be left with $3.37 gal gal 3.7 L $ L Multiply the numerators. Multiply the denominators. $ L price ($) L in the final answer. $ L 7

8 Divide the numerator by the denominator. Round to the nearest cent. $ L $0.8 per liter You Try It : The price of gas is $4.28 per gallon. Find the price per liter. Example 6: The speed limit on a highway in Montreal is 20 kilometers per hour. How fast is this in miles per hour? Round your answer to the nearest tenth if necessary. Rewrite each per statement: 20 kilometers per hour = 20 km hr Now we can see that the problem wants us to convert 20 miles per hour = mi hr km to mi hr hr. Notice that there are two types of units involved: length and time Both times are already in hours so we only need to perform one conversion: kilometers Choose the appropriate unit fraction and attach it to the right of what is given. miles Attach mi.6 km to convert kilometers to miles. 20 km mi hr.6 km 8

9 Now divide out units to make sure you will be left with mi hr in the final answer. 20 km mi hr. 6 km 20 mi hr.6 Multiply the numerators. Multiply the denominators. 20 mi.6 hr 20 mi.6 km Divide the numerator by the denominator. Round to the nearest tenth mi hr 74. miles per hour You Try It 6: The speed limit on a road in Montreal is 7 kilometers per hour. How fast is this in miles per hour? Round your answer to the nearest tenth if necessary.

10 Temperature When you travel outside of the United States. length, mass, and volume are not the only measurements that differ. In the U.S., temperature is measured in degrees Fahrenheit ( F ). Scientists and the rest of the world use degrees Celsius ( C ) to measure temperature. Because of this, temperature measured in Celsius is categorized as belonging to the metric system, while temperature measured in Fahrenheit is categorized as belonging to the U.S. Customary system. Two of the most important benchmarks that help us understand the degrees Celsius in relation to degrees Fahrenheit are the freezing and boiling points of water. Freezing and Boiling Points of Water Water freezes at 0 degrees Celsius ( 0 C ). This is 32 degrees Fahrenheit (32 F ). Water boils at 00 degrees Celsius (00 C ). This is 22 degrees Fahrenheit ( 22 F ). Here are some typical measurements in both Celsius and Fahrenheit: Celsius Fahrenheit water boils 00 C 22 F hot coffee 60 C 40 F hot bath water 0 C 22 F normal body temperature 37 C 8.6 F summer day 30 C 86 F room temperature 20 C 68 F winter day in California 0 C 0 F water freezes 0 C 32 F super cold winter day 8 C 0 F 0

11 Example 7: Circle the most reasonable metric temperature for each situation. a) Warm summer day: 2 C 64 C 0 C b) Iced tea: C C 30 C a) 2 C because the other temperatures are both above the temperature of hot coffee. Way too hot! b) C because C is below freezing which means that the tea would be frozen solid and 30 C is the temperature of a warm summer day which means that the tea would no longer be iced tea. You Try It 7: Circle the most reasonable metric temperature for each situation. a) Inside a freezer: 0 C C 2 C b) Set the living room thermostat at: 8 C 2 C 7 C c) Wear a jacket outside because it is: 2 C 28 C 0 C Now that we have a better understanding of Celsius-Fahrenheit relationships we can look at using formulas to convert back and forth between Celsius and Fahrenheit. Celsius and Fahrenheit Conversion Formulas Converting from F to C F 32 C Converting from C F C32 to F Remember, once you plug in the given temperature to the formula, use the order of operations to simplify. Use your calculator to help with any computations that involve fractions or decimals.

12 Example 8: Convert 20 F to Celsius. Round your answer to the nearest degree if necessary. Since we want to find Celsius, write the formula that already has C isolated on one side. Substitute F 20 into the formula. Use the order of operations to simplify. C F 32 C Perform the subtraction inside the parentheses first. Now multiply. Round to the nearest degree. C 2 20 C 3 C 6.6 C 7 You Try It 8: Convert F to Celsius. Round your answer to the nearest degree if necessary. 2

13 Example : Convert 2 C to Fahrenheit. Round your answer to the nearest degree if necessary. Since we want to find Fahrenheit, write the formula that already has F isolated on one side. F C 32 Substitute C 2 into the formula. Use the order of operations to simplify. Perform the multiplication first. Now add. F 2 32 F 4 32 F 77 You Try It : Convert 32 C to Fahrenheit. Round your answer to the nearest degree if necessary. 3