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Converting Units: Understanding Dimensional Analysis and Practical Applications

This lesson focuses on unit conversion techniques using dimensional analysis. Learn how to convert miles to feet, kilometers to minutes, and gallons to quarts. Through examples, such as converting 0.7 miles to feet (3,696 ft) and a rowing team's speed of 6.84 m/s to kilometers per minute (0.4104 km/min), you’ll develop skills to choose appropriate units for various scenarios. The lesson also emphasizes estimating and checking the reasonableness of conversions, rounding to compatible numbers, and applying conversion factors effectively.

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Converting Units: Understanding Dimensional Analysis and Practical Applications

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  1. Multiply by a conversion factor. 0.7 mi 1 5,280 ft 1 mi 0.7 mi = • Divide by the common units. (0.7)(5,280) ft 1 = Simplify. Simplify. = 3,696 ft COURSE 3 LESSON 5-2 Choosing and Converting Units Use dimensional analysis to convert 0.7 mi to ft. There are 3,696 ft in 0.7 miles. 5-2

  2. Estimate 6.84 7. Then, 7 • 60 ÷ 1000 = 0.42. Multiply by two ratios that each equal one. 6.84 m 1 s 6.84 m 1 s 1 km 1000 m 60 s 1 min = • • Divide by the common units. (6.48)(1)(60) km (1)(1,000)(1) min = Simplify. Use a calculator. = 0.4104 COURSE 3 LESSON 5-2 Choosing and Converting Units A rowing team completed a 2,000-m course at a rate of 6.84 m/s. Convert this rate to kilometers per minute. The team rowed at a rate of 0.4104 km/min. Check for Reasonableness The answer 0.4104 km/min is close to the estimate 0.42. The answer is reasonable. 5-2

  3. Round to the nearest number divisible by 4. 33 qt 32 qt 32 qt 1 1 gal 4 qt Multiply by the conversion factor. = • Divide by the common units. 32 4 = gallons Simplify. Divide. = 8 gallons COURSE 3 LESSON 5-2 Choosing and Converting Units Use compatible numbers to estimate the number of gallons in 33 quarts. 1 gal 4 qt The conversion factor for changing gallons to quarts is . There are about 8 gallons in 33 quarts. 5-2

  4. COURSE 3 LESSON 5-2 Choosing and Converting Units 1. Choose an appropriate customary unit and metric unit for the distance between two cities. 2. Convert 0.75 hours to seconds. 3. $150 per hour is how much per minute? 4. 69.2 cm is about how many meters? miles; kilometers 2,700 s $2.50 per min 0.7 m 5-2

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