We need to convert 2.5 gallons to quarts using the given conversion factor. Set up the conversion using dimensional analysis: 2.5 gallons × (4 quarts / 1 gallon). The gallons cancel out, leaving us with: 2.5 × 4 quarts = 10 quarts. A common error is dividing by 4 instead of multiplying when converting from gallons to quarts. Since quarts are smaller units than gallons, we expect more quarts than gallons.

We need to convert 60 miles per hour to feet per second using two conversion factors. Set up the conversion using dimensional analysis: 60 mph × (5280 ft / 1 mile) × (1 hour / 3600 sec). The miles and hours cancel out, leaving: (60 × 5280) / 3600 ft/s. Calculate: 316,800 / 3600 = 88 ft/s. A common error is using incorrect conversion factors or forgetting to convert both the distance and time units. Always track units carefully through each step to ensure proper cancellation.

We need to convert 3 hours to seconds using two successive conversions through minutes. Set up the conversion using dimensional analysis: 3 hours × (60 min / 1 hour) × (60 sec / 1 min). Both hours and minutes cancel out, leaving: 3 × 60 × 60 sec = 10,800 seconds.

We need to convert 2 quarts to cups using the US customary system conversion factor. Set up the conversion: 2 quarts × (4 cups/1 quart). Calculate: 2 × 4 = 8 cups, with the quart units canceling out properly. The essential conversion factor is that 1 quart = 4 cups in the US measurement system. Students often confuse this with pints (1 quart = 2 pints) or gallons (4 quarts = 1 gallon). For US liquid measurements, remember the hierarchy: cup → pint → quart → gallon with factors of 2, 2, and 4 respectively.

We need to convert 4 pounds to ounces using the US customary weight conversion factor. Set up the conversion: 4 pounds × (16 oz/1 pound). Calculate: 4 × 16 = 64 ounces, with the pound units canceling out properly. The crucial conversion factor is that 1 pound = 16 ounces in the US weight system. Students sometimes mistakenly use 12 (confusing with inches per foot) or 8 (half the correct value). Remember that weight conversions in the US system use 16 ounces per pound, unlike the more systematic factors of 10 in the metric system.

We need to convert 5 kilometers to meters using the given conversion factor. Set up the conversion using 1 kilometer = 1000 meters as our conversion factor. Using dimensional analysis: 5 kilometers × (1000 meters/1 kilometer) = 5000 meters. The kilometers units cancel out, leaving us with meters. A common error would be dividing by 1000 instead of multiplying, which would give 0.005 meters. When converting from a larger unit (kilometers) to a smaller unit (meters), always multiply by the conversion factor.

We need to convert 2 cups to liters using the given conversion factor of 1 cup = 0.236 liters. Set up the conversion with the given factor: 1 cup = 0.236 liters. Using dimensional analysis: 2 cups × (0.236 liters/1 cup) = 0.472 liters. The cups units cancel out, leaving us with liters as our final unit. Students might mistakenly divide 2 by 0.236 or confuse the conversion direction. Remember to set up the conversion factor so the unwanted units cancel out properly.

We need to convert 10 kilometers to meters using the metric system conversion factor. Set up the conversion: 10 kilometers × (1000 m/1 km). Calculate: 10 × 1000 = 10,000 meters, with the kilometer units canceling out to leave meters. The key metric conversion is that 1 kilometer = 1000 meters, since 'kilo' means 1000. A common error is using 100 instead of 1000, confusing kilometers with hectometers. In metric conversions, always check the prefix: kilo = 1000, hecto = 100, deka = 10, and the base unit has no prefix.

We need to convert 3000 square meters to square kilometers using the linear conversion 1 km = 1000 m. Set up the area conversion by squaring the linear conversion factor: (1 km)² = (1000 m)², so 1 km² = 1,000,000 m². Using dimensional analysis: 3000 m² × (1 km²/1,000,000 m²) = 0.003 km². The square meter units cancel out, leaving square kilometers. A critical error is using the linear conversion factor (1000) instead of the squared factor (1,000,000) for area conversions. Always square the linear conversion factor when working with area units.

We need to convert 60 miles per hour to feet per second using two conversion factors. Set up the conversion using both given factors: 1 mile = 5280 feet and 1 hour = 3600 seconds. Using dimensional analysis: 60 mph × (5280 feet/1 mile) × (1 hour/3600 seconds) = (60 × 5280)/3600 feet per second. Calculate: 316,800/3600 = 88 feet per second. Students often forget to convert hours to seconds in the denominator or mix up the conversion factors. Always ensure units cancel properly in dimensional analysis problems involving compound units.