Complete the table to convert the units.
| | Initial quantity | Initial Units | x | First ratio | Units | x | Second ratio | Units | x | Third ratio | Units | - | Final quantity | Final Units |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Example | 25 | fl oz/kg | x | 29.574 | mL/fl oz | x | 0.454 | kg/lb | | | | | 335.358 | mL/lb |
| A | 2.5 | g/L | x | | | x | | | | | | | | |
| B | 5 | m^2/mL | x | | | x | | | x | | | - | | |
| C | 46.2 | fl oz/kg | x | | | x | | | | | | | | |
| D | 33.0 | m^2/kg | x | | | x | | | x | | | - | | |
Answer (2)
Convert grams per liter to ounces per gallon: 2.5 L g × 28.3495 g 1 oz × 1 g a l 3.78541 L = 0.3338 g a l oz .
Convert square meter per mililiter to square feet per teaspoon: 5 m L m 2 × 1 m 2 ( 3.28084 f t ) 2 × 0.202884 t s p 1 m L = 265.2725 t s p f t 2 .
Convert fluid ounces per kilogram to milliliters per pound: 46.2 k g f l oz × 1 f l oz 29.5735 m L × 2.20462 l b 1 k g = 619.7420 l b m L .
Convert square meters per kilogram to square feet per pound: 33.0 k g m 2 × 1 m 2 ( 3.28084 f t ) 2 × 2.20462 l b 1 k g = 161.1203 l b f t 2 .
Explanation
Understanding the Problem We are given a table with conversion problems. We need to complete the table by finding the final quantities and units for problems A, B, C, and D. We will use the conversion factors to convert the initial units to the final units.
Solving A A) Convert grams per liter to ounces per gallon: We have 2.5 L g . We want to convert this to g a l oz . We know that 1 oz = 28.3495 g and 1 L = 0.264172 g a l or 1 g a l = 3.78541 L .
So, we have: 2.5 L g × 28.3495 g 1 oz × 1 g a l 3.78541 L = 28.3495 2.5 × 3.78541 g a l oz = 0.3338 g a l oz
Solving B B) Convert square meter per milliliter to square feet per teaspoon: We have 5 m L m 2 . We want to convert this to t s p f t 2 . We know that 1 m = 3.28084 f t and 1 m L = 0.202884 t s p .
So, we have: 5 m L m 2 × 1 m 2 ( 3.28084 f t ) 2 × 0.202884 t s p 1 m L = 0.202884 5 × ( 3.28084 ) 2 t s p f t 2 = 265.2725 t s p f t 2
Solving C C) Convert fluid ounces per kilogram to milliliters per pound: We have 46.2 k g f l oz . We want to convert this to l b m L . We know that 1 f l oz = 29.5735 m L and 1 k g = 2.20462 l b .
So, we have: 46.2 k g f l oz × 1 f l oz 29.5735 m L × 2.20462 l b 1 k g = 2.20462 46.2 × 29.5735 l b m L = 619.7420 l b m L
Solving D D) Convert square meters per kilogram to square feet per pound: We have 33.0 k g m 2 . We want to convert this to l b f t 2 . We know that 1 m = 3.28084 f t and 1 k g = 2.20462 l b .
So, we have: 33.0 k g m 2 × 1 m 2 ( 3.28084 f t ) 2 × 2.20462 l b 1 k g = 2.20462 33.0 × ( 3.28084 ) 2 l b f t 2 = 161.1203 l b f t 2
Final Answer Therefore, the final quantities and units are: A) 0.3338 g a l oz B) 265.2725 t s p f t 2 C) 619.7420 l b m L D) 161.1203 l b f t 2
Examples
Unit conversion is a fundamental skill in many real-world applications. For instance, when cooking, you might need to convert grams to ounces or milliliters to cups. In construction, converting square meters to square feet is essential for accurate material calculations. Similarly, in chemistry and physics, converting between different units of measurement is crucial for performing calculations and understanding experimental results. Mastering unit conversion allows for accurate and efficient problem-solving in various fields, ensuring precision and consistency in measurements and calculations.
The final quantities after performing the conversions are: A) 0.3338 oz/gal, B) 265.2725 ft²/tsp, C) 619.7420 mL/lb, D) 161.1203 ft²/lb.
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