Determine the volume in liters of a 1.00 ounce bottle. (1.06 qt. = 1 L; 32 ounces= 1 qt)
The Correct Answer and Explanation is:
Correct Answer:
The volume of a 1.00-ounce bottle is approximately 0.03125 liters.
Explanation:
To determine the volume in liters of a 1.00-ounce bottle, a step-by-step unit conversion can be applied. The known conversion relationships are:
- 32 ounces = 1 quart
- 1.06 quarts = 1 liter
First, the volume in ounces must be converted to quarts:1.00 oz32 oz per qt=0.03125 qt\frac{1.00 \, \text{oz}}{32 \, \text{oz per qt}} = 0.03125 \, \text{qt}32oz per qt1.00oz=0.03125qt
Next, the result in quarts is converted to liters using the conversion factor between quarts and liters:0.03125 qt1.06 qt per L=0.02948 L (rounded to 5 significant figures)\frac{0.03125 \, \text{qt}}{1.06 \, \text{qt per L}} = 0.02948 \, \text{L (rounded to 5 significant figures)}1.06qt per L0.03125qt=0.02948L (rounded to 5 significant figures)
This gives a result of approximately 0.02948 liters.
However, a more precise and direct route gives a general formula:Liters=(Ounces32)×(11.06)\text{Liters} = \left(\frac{\text{Ounces}}{32}\right) \times \left(\frac{1}{1.06}\right)Liters=(32Ounces)×(1.061)
Substituting 1 ounce into the formula:Liters=(132)×(11.06)≈0.02948\text{Liters} = \left(\frac{1}{32}\right) \times \left(\frac{1}{1.06}\right) \approx 0.02948Liters=(321)×(1.061)≈0.02948
Thus, 1.00 fluid ounce corresponds to approximately 0.0295 liters.
Alternatively, to simplify the understanding of the proportion:
Since 1 quart contains 32 ounces and 1 liter equals 1.06 quarts, it follows that:1 oz=132 qt=132×1.06 L≈0.0295 L1 \, \text{oz} = \frac{1}{32} \, \text{qt} = \frac{1}{32 \times 1.06} \, \text{L} \approx 0.0295 \, \text{L}1oz=321qt=32×1.061L≈0.0295L
Understanding such unit conversions proves essential in scientific measurements, cooking, and international commerce, where various systems of measurement are still in use.
