Weight 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 ounce, 1 pound, 1 short ton, and 1 long ton to common metric measures. The second shows the equivalency of 1 milligram, 1 gram, 1 kilogram, and 1 metric ton to common U.S. Customary measurements. For ease in use, we have rounded the measurements to two decimal places where possible. Milligrams Grams Kilograms Metric Ton 1 Ounce 28349.52 28.35 0.03 0.00003 1 Pound 453592.37 453.59 0.45 0.0005 1 Short Ton (2000 lbs. US) 907184740 907184.74 907.18.91 1 Long Ton (2240 lbs. UK) 1016046908.8 1016046.91 1016.05 1.02 Ounce Pound Short Ton Long Ton 1 Milligram 0.00004 0.000002 - - - - - - 1 Gram 0.04 0.002 0.000001 - - - 1 Kilogram 35.27 2.20 0.001 0.001 1 Metric Ton 35273.96 2204.62 1.10 0.98 One important thing to remember is that the U.S. Customary measurements measure weight, which depends upon the pull of gravity. The metric system measures mass, which is the same regardless of what the pull of gravity is. In other words the mass would be the same on Earth and on the moon, but the weight would be different. For our purposes, we are using the gravity of Earth to do our conversions. 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.
Activity One: If we know that 1 ounce (oz.) = 28.35 grams (g) or.03 kilograms (kg), find the answers to the following problems. 6 oz. = g 12 oz. = kg 20 oz. = g 48 oz. = kg 14 oz. = g 42 oz. = kg 56 oz. = g 36 oz. = kg 39 oz. = g 25 oz. = kg Activity Two: Now that you have your answers for the above problems, convert them into metric measurements. For example, we see that 6 oz. equals 170.10 g. There are 1000 grams in a kilogram. To convert from grams to kilograms, you divide the number of grams by 1000, so 6 oz. also equals 0.17 kg. To convert from kilograms to grams, you multiply the number of kilograms by 1000. Using your answers in the exercise above, convert the gram answers to kilograms and the kilogram answers to grams. Round your answers to two decimal places. The first one is done for you. 6 oz. = 170.10 g or 0.17 kg 12 oz. = kg or g 20 oz. = g or kg 48 oz. = kg or g 14 oz. = g or kg 42 oz. = kg or g 56 oz. = g or kg 36 oz. = kg or g 39 oz. = g or kg 25 oz. = kg or g
Activity Three: If we know that 1 g equals.04 oz., convert the following: 18 g = oz. 10 g = oz. 95 g = oz. 600 g = oz. 276 g = oz. 183 g = oz. 409 g = oz. 382 g = oz. 761 g = oz. 873 g = oz. Activity Four: Using the fact that 1 pound (lb.) equals.45 kilograms (kg) or 453.59 g, find the answers to the following problems: 1. If you were buying 3 lbs. of cheese at the deli, how many kilograms of cheese would you need? How many grams? 2. If you were required to fill out a form showing your weight in kilograms, how much would you weigh if you weighed 110 lbs.? How many grams would you weigh? 3. You are having a party and need to buy 2 lbs. of lunch meat for every 6 people at the party. There will be 24 people at the party. How many lbs. of lunch meat do you need to buy? How many kilograms would that equal? How many grams? 4. You just pulled a muscle in your arm and the doctor tells you not to lift anything heavier than 5 lbs. How many kilograms can you lift? 5. The weight machine at the gym is set up with 150 lbs. on it. How many kilograms is on the weight machine?
Activity Five: Now, using the fact that 1 kg = 2.20 lbs., compute the following: 34 kg = lbs. 57 kg = lbs. 76 kg = lbs. 61 kg = lbs. 48 kg = lbs. 12 kg = lbs. 29 kg = lbs. 23 kg = lbs. 17 kg = lbs. 52 kg = lbs. Activity Six: Using the fact that 1 U.S. ton (2000 lbs.) equals.91 metric tons, do the following problems: 1. You are talking to a friend who delivers topsoil. You decide you need to get 6 tons of topsoil. How many metric tons of topsoil do you need? 2. You see a sign that says the road ahead is only open to vehicles weighing less than 10 tons. How many metric tons, maximum, can a vehicle weigh and still travel on the road? 3. You are delivering gravel to a work site not far from where you work. The call comes in that they need 25 tons of gravel delivered as soon as possible. How many metric tons of gravel do they need? 4. Your job is to deliver coal to a company that ships it out of the area. On Monday, you deliver 16 tons of coal; on Tuesday, you deliver 30 tons of coal; on Wednesday, you deliver 21 tons of coal; and on Thursday, you deliver 14 tons of coal. How many metric tons of coal did you deliver altogether? 5. You are driving a truck and come to an intersection. The road to the left allows vehicles that weigh a maximum of 16 tons on it. The road to the right allows vehicles with a maximum weight of 20 tons. Both roads will get you where you are going, but you take the road on the right because of the weight of your truck. How many more metric tons are allowed on the road to the right?
Activity Seven: Knowing that 1 metric ton =.98 long ton (UK ton = 2240 lbs.), do the following problems: 65 metric tons = long tons 72 metric tons = long tons 32 metric tons = long tons 84 metric tons = long tons 45 metric tons = long tons 29 metric tons = long tons 21 metric tons = long tons 37 metric tons = long tons 16 metric tons = long tons 62 metric tons = long tons
Answer Key: Activity One: 6 oz. = 170.1 g 12 oz. = 0.36 kg 20 oz. = 567 g 48 oz. = 1.44 kg 14 oz. = 396.9 g 42 oz. = 1.26 kg 56 oz. = 1587.6 g 36 oz. = 1.08 kg 39 oz. = 1105.65 g 25 oz. =.75 kg Activity Two: 6 oz. = 170.1 g or 0.17 kg 12 oz. = 0.36 kg or 340 g 20 oz. = 567 g or 0.57 kg 48 oz. = 1.44 kg or 1440 g 14 oz. = 396.9 g or.40 kg 42 oz. = 1.26 kg or 1260 g 56 oz. = 1587.6 g or 1.59 kg 36 oz. = 1.08 kg or 1080 g 39 oz. = 1105.65 g or 1.11 kg 25 oz. =.75 kg or 750 g Activity Three: 18 g =.72 oz. 10 g =.4 oz. 95 g = 3.8 oz. 600 g = 24 oz. 276 g = 11.04 oz. 183 g = 7.32 oz. 409 g = 16.36 oz. 382 g = 15.28 oz. 761 g = 30.44 oz. 873 g = 34.92 oz. Activity Four: 1. 1.35 kg or 1360.77 g 2. 49.5 kg or 49894.9 g 3. 3.6 kg or 3628.72 g 4. 2.25 kg 5. 67.5 kg
Activity Five: 34 kg = 74.8 lbs. 57 kg = 125.4 lbs. 76 kg = 167.2 lbs. 61 kg = 134.2 lbs. 48 kg = 105.6 lbs. 12 kg = 26.4 lbs. 29 kg = 63.8 lbs. 23 kg = 50.6 lbs. 17 kg = 37.4 lbs. 52 kg = 114.4 lbs. Activity Six: 1. 5.46 metric tons 2. 9.1 metric tons 3. 22.75 metric tons 4. 73.71 metric tons 5. 3.64 metric tons Activity Seven: 65 metric tons = 63.7 long tons 72 metric tons = 70.56 long tons 32 metric tons = 31.36 long tons 84 metric tons = 82.32 long tons 45 metric tons = 44.1 long tons 29 metric tons = 28.42 long tons 21 metric tons = 20.58 long tons 37 metric tons = 36.26 long tons 16 metric tons = 15.68 long tons 62 metric tons = 60.76 long tons