The question requires converting 2.5 gallons of lemonade to quarts, using the factor 1 gallon = 4 quarts. Set up the conversion: 2.5 gallons × (4 quarts / 1 gallon). Calculate: 2.5 × 4 = 10 quarts, with gallons canceling to leave quarts. Dimensional analysis helps by showing unit cancellation: gallons in the numerator and denominator cancel, resulting in quarts. A common error is confusing the factor and dividing instead of multiplying, which would give 0.625 quarts incorrectly. Ensure you apply the conversion in the correct direction for the units needed. For test-taking, verify the arithmetic is simple multiplication to avoid calculator dependency.

The task is to convert 420 kilometers (km) to meters (m), using 1 km = 1000 m. Set up the conversion: 420 km × (1000 m / 1 km). Calculate: 420 × 1000 = 420,000 m, with km canceling to leave m. Dimensional analysis shows km × m/km = m, confirming units. A key error is dividing by 1000, yielding 0.42 m incorrectly. Remember to multiply when going to smaller units. In tests, check the magnitude—km to m should increase the number.

The question requires converting a volume of 0.15 cubic meters (m³) to liters (L), using 1 m = 100 cm and 1000 cm³ = 1 L, cubing for volume. Set up: 0.15 m³ × (100 cm / 1 m)³ × (1 L / 1000 cm³) = 0.15 × 1,000,000 × (1/1000) = 0.15 × 1,000 = 150 L. Calculate: (100)³ = 1,000,000 cm³/m³, then /1000 = 1,000 L/m³, so 0.15 × 1,000 = 150 L, with m³ to cm³ to L. Dimensional analysis tracks: m³ × (cm/m)³ × L/cm³ = L, ensuring cancellation. A common error is not cubing, leading to 15 L or similar. For volumes, always cube length factors.

The problem asks to convert a speed of 150 feet in 2.5 seconds to miles per hour (mph), using 1 mile = 5280 ft and 1 hour = 3600 s. First, find ft/s: 150 ft / 2.5 s = 60 ft/s; then convert: 60 ft/s × (3600 s / 1 h) × (1 mi / 5280 ft) = (60 × 3600) / 5280 = 216,000 / 5280 ≈ 40.909 mph. Dimensional analysis: ft/s × s/h × mi/ft = mi/h, with units canceling properly. A key error is forgetting to convert both units, like only time, yielding wrong values. Calculate step-by-step for precision. As a strategy, compute speed in ft/s first, then apply conversions separately.

The task is to convert 14 quarts (qt) to gallons (gal), using 1 gal = 4 qt. Set up the conversion: 14 qt × (1 gal / 4 qt). Calculate: 14 / 4 = 3.5 gal, with qt canceling to leave gal. Dimensional analysis tracks qt × gal/qt = gal, confirming the result. A key error is multiplying by 4, giving 56 gal, or stopping at partial conversion. Ensure full application of the factor. As a strategy, verify if the result makes sense—14 qt should be more than 3 gal but less than 4.

The question is to convert 180 centimeters (cm) to meters (m), using 100 cm = 1 m. Set up the conversion: 180 cm × (1 m / 100 cm). Calculate: 180 / 100 = 1.8 m, with cm canceling to leave m. Dimensional analysis shows cm × m/cm = m, ensuring correct units. A common error is multiplying by 100, yielding 18,000 m incorrectly, as warned. Always divide when converting to larger units. For test-taking, think of the prefix centi- meaning 1/100 to guide the operation.

The problem requires converting 2.25 pounds (lb) to ounces (oz), using 1 lb = 16 oz. Set up the conversion: 2.25 lb × (16 oz / 1 lb). Calculate: 2.25 × 16 = 36 oz, with lb canceling to leave oz. Dimensional analysis confirms lb × oz/lb = oz, tracking units simply. A key error is dividing by 16, giving 0.1406 oz incorrectly. Remember to multiply when going to smaller units. In tests, recall that 16 oz per lb is standard for weight conversions.

The task involves converting 96 inches (in) to yards (yd), using 12 in = 1 ft and 3 ft = 1 yd, requiring two steps. Set up the chained conversion: 96 in × (1 ft / 12 in) × (1 yd / 3 ft). Calculate: first, 96 / 12 = 8 ft, then 8 / 3 ≈ 2.6667 yd, or exactly 96 / (12 × 3) = 96 / 36 = 2.6667 yd. Dimensional analysis tracks: in × ft/in × yd/ft = yd, with units canceling step-by-step. A key error is forgetting one step, like only dividing by 12 to get 8 ft, not yd. Another mistake is multiplying instead of dividing. For multi-step conversions, write out all factors in one expression to ensure accuracy.

The question is to convert a volume of 750 milliliters (mL) to liters (L), using 1000 mL = 1 L. Set up the conversion: 750 mL × (1 L / 1000 mL). Calculate: 750 / 1000 = 0.75 L, with mL canceling to leave L. Dimensional analysis shows mL × L/mL = L, ensuring proper tracking. A common error is multiplying by 1000, giving 750,000 L incorrectly. Remember, going to larger units means dividing. In tests, use the prefix milli- (1/1000) to guide the direction.

The problem asks to convert a video length of 2 hours 18 minutes to total minutes, using 60 minutes = 1 hour. Set up the conversion for hours: 2 hours × (60 min / 1 h) + 18 min. Calculate: 2 × 60 = 120, then 120 + 18 = 138 min, with hours canceling in the first part. Dimensional analysis for the hours part: h × min/h = min, then add the remaining min. A key error is treating 18 min as 0.18 hours and converting wrongly, like 2.18 × 60 = 130.8, but that's incorrect. Convert hours fully before adding minutes. As a strategy, break mixed units into separate conversions to avoid confusion.