Select all possible conversion factors between the units of deciliters and liters. 1 L/10 dL 1 dL/ 10-3L.
The Correct Answer and Explanation is :
To determine the conversion factors between deciliters (dL) and liters (L), we start with the definitions of these units:
- Liter (L): The liter is a unit of volume in the metric system, commonly used to measure liquids.
- Deciliter (dL): A deciliter is one-tenth of a liter. Therefore, (1 \, \text{dL} = 0.1 \, \text{L}) or equivalently (1 \, \text{L} = 10 \, \text{dL}).
Possible Conversion Factors
- From liters to deciliters:
- The relationship (1 \, \text{L} = 10 \, \text{dL}) implies that:
[
\text{Conversion factor} = \frac{1 \, \text{L}}{10 \, \text{dL}}
] - This factor can be used to convert liters into deciliters by multiplying the volume in liters by 10.
- From deciliters to liters:
- Conversely, since (1 \, \text{dL} = 0.1 \, \text{L}), we can express this relationship as:
[
\text{Conversion factor} = \frac{1 \, \text{dL}}{0.1 \, \text{L}} = \frac{1 \, \text{dL}}{10^{-1} \, \text{L}} = 10 \, \text{dL} = 1 \, \text{L}
] - This means:
[
\text{Conversion factor} = \frac{1 \, \text{dL}}{10^{-1} \, \text{L}} = 1 \, \text{dL} \cdot \frac{10^{3}}{1} \, \text{L} = \frac{1 \, \text{dL}}{10^{-3} \, \text{L}} = 1000 \, \text{dL} = 1 \, \text{L}
]
Summary
The possible conversion factors between deciliters and liters are:
- (\frac{1 \, \text{L}}{10 \, \text{dL}})
- (\frac{1 \, \text{dL}}{0.1 \, \text{L}}) or equivalently, (\frac{1 \, \text{dL}}{10^{-1} \, \text{L}})
Using these conversion factors allows for easy calculations between the two units, facilitating accurate measurement in various contexts, such as cooking, laboratory work, and general liquid measurement. Understanding these conversions is essential for anyone working in fields that require precise volume measurements.