Verified Answer :
- Conversion factors are applied using dimensional analysis (multiplying by the ratio of units).
- Results for the specific conversions:
- 8 inches: \(\boxed{2/3 \text{ ft}}\)
- 6 yards: \(\boxed{18 \text{ ft}}\)
- 24 fl oz: \(\boxed{1.5 \text{ pt}}\)
- 3.7 kg: \(\boxed{8.15709 \text{ lb}}\)
- 4.2 km: \(\boxed{4200 \text{ m}}\)
- 285 g: \(\boxed{0.285 \text{ kg}}\)
- 0.75 kg: \(\boxed{750,000 \text{ mg}}\)
- 1.9 L: \(\boxed{2.00771 \text{ qt}}\)
Explanation
- Analysis of Unit Conversions
To convert measurements between units, we use established conversion factors. The process involves identifying the relationship between the original unit and the desired unit, then multiplying or dividing by the appropriate conversion factor so that the original unit cancels out. We will address each conversion individually.
- Performing Calculations
For the given conversions:
- To convert 8 inches to feet, use 1 foot = 12 inches:
\(8 \text{ in.} \times \frac{1 \text{ ft}}{12 \text{ in.}} = \frac{8}{12} \text{ ft} = \frac{2}{3} \text{ ft} \approx 0.67 \text{ ft}\).
- To convert 6 yards to feet, use 1 yard = 3 feet:
\(6 \text{ yd} \times \frac{3 \text{ ft}}{1 \text{ yd}} = 18 \text{ ft}\).
- To convert 24 fluid ounces to pints, use 1 pint = 16 fluid ounces:
\(24 \text{ fl oz} \times \frac{1 \text{ pt}}{16 \text{ fl oz}} = \frac{24}{16} \text{ pt} = 1.5 \text{ pt}\).
- To convert 3.7 kilograms to pounds, use 1 kg \(\approx\) 2.20462 lb:
\(3.7 \text{ kg} \times 2.20462 \text{ lb/kg} \approx 8.15709 \text{ lb}\).
- To convert 4.2 kilometers to meters, use 1 kilometer = 1000 meters:
\(4.2 \text{ km} \times 1000 \text{ m/km} = 4200 \text{ m}\).
- To convert 285 grams to kilograms, use 1 kilogram = 1000 grams:
\(285 \text{ g} \times \frac{1 \text{ kg}}{1000 \text{ g}} = 0.285 \text{ kg}\).
- To convert 0.75 kilograms to milligrams, use 1 kg = 1000 g and 1 g = 1000 mg:
\(0.75 \text{ kg} \times 1000 \text{ g/kg} \times 1000 \text{ mg/g} = 750,000 \text{ mg}\).
- To convert 1.9 liters to quarts, use 1 liter \(\approx\) 1.05669 quarts:
\(1.9 \text{ L} \times 1.05669 \text{ qt/L} \approx 2.00771 \text{ qt}\).
- Conclusion and Final Answers
Based on the calculations above, the final results are:
- \(8 \text{ in.} = \boxed{\frac{2}{3} \text{ ft}}\) (or approximately \(0.67 \text{ ft}\))
- \(6 \text{ yd} = \boxed{18 \text{ ft}}\)
- \(24 \text{ fl oz} = \boxed{1.5 \text{ pt}}\)
- \(3.7 \text{ kg} = \boxed{8.15709 \text{ lb}}\)
- \(4.2 \text{ km} = \boxed{4200 \text{ m}}\)
- \(285 \text{ g} = \boxed{0.285 \text{ kg}}\)
- \(0.75 \text{ kg} = \boxed{750,000 \text{ mg}}\)
- \(1.9 \text{ L} = \boxed{2.00771 \text{ qt}}\)
Examples
In daily life, understanding unit conversions is essential for tasks like cooking, traveling, and construction. For example, if a recipe calls for 1.9 liters of water and you have a measuring jug that only shows quarts, knowing that 1.9 liters is approximately 2.008 quarts allows you to follow the recipe accurately. Similarly, if you are planning a trip to a country that uses kilometers while your car's odometer measures in miles or your GPS displays in meters, being able to convert between these units ensures you reach your destination without confusion. Developing these skills makes navigating different measurement systems quick and intuitive.