convert 1.60 x 104 mL to quarts (qt) using dimensional analysis.
The Correct Answer and Explanation is:
To convert 1.60×104 mL1.60 \times 10^4 \, \text{mL}1.60×104mL to quarts (qt) using dimensional analysis, we will use the following conversion factors:
- 1 liter (L) = 1000 milliliters (mL)
- 1 quart (qt) = 0.946353 liters (L)
Step-by-step conversion:
- Start with the given value:
1.60×104 mL1.60 \times 10^4 \, \text{mL}1.60×104mL - Convert milliliters (mL) to liters (L): 1.60×104 mL×1 L1000 mL=16.0 L1.60 \times 10^4 \, \text{mL} \times \frac{1 \, \text{L}}{1000 \, \text{mL}} = 16.0 \, \text{L}1.60×104mL×1000mL1L=16.0L
- Convert liters (L) to quarts (qt): 16.0 L×1 qt0.946353 L=16.00.946353 qt=16.91 qt16.0 \, \text{L} \times \frac{1 \, \text{qt}}{0.946353 \, \text{L}} = \frac{16.0}{0.946353} \, \text{qt} = 16.91 \, \text{qt}16.0L×0.946353L1qt=0.94635316.0qt=16.91qt
Final result:
So, 1.60×104 mL1.60 \times 10^4 \, \text{mL}1.60×104mL is equivalent to approximately 16.91 quarts.
Explanation of Dimensional Analysis:
Dimensional analysis is a method used to convert units by multiplying by conversion factors that cancel out the units you don’t need, leaving you with the desired units. In this case, we first convert milliliters to liters and then liters to quarts. The conversion factors are carefully chosen based on the relationships between the units involved, ensuring that the units “cancel out” in the right order. This method is not only straightforward but also reliable in converting between different units.
