How is using a conversion factor different from using proportions to convert measurement units? Explain which is easier and why.
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Using a conversion factor and using proportions are both methods of converting measurement units, but they differ in their approach and ease of use.
Conversion factors involve multiplying the given value by a ratio that relates the two units being converted. These ratios are derived from the equivalence between different units, such as 1 meter being equal to 3.281 feet. By multiplying the given value by the appropriate conversion factor, the desired unit can be obtained. For example, to convert 2 meters to feet, the conversion factor of 3.281 feet per meter would be used: 2 meters * 3.281 feet/meter = 6.562 feet.
Using proportions, on the other hand, involves setting up an equation with ratios of equivalent quantities and solving for the unknown variable. For example, to convert 2 meters to feet, a proportion can be set up with the ratios of meters to feet: 2 meters / x feet = 1 meter / 3.281 feet. Solving for x, the unknown variable representing the desired measurement in feet, you would cross-multiply and divide: 2 meters * 3.281 feet = 1 meter * x feet, resulting in x = 6.562 feet.
Considering the ease of use, using conversion factors is generally easier and more straightforward compared to proportions. Conversion factors only require multiplication by a known ratio, whereas proportions involve setting up equations and solving for the unknown variable. This means that using conversion factors involves fewer steps and calculations, making it simpler and less prone to errors.
Moreover, conversion factors provide a direct relationship between the units being converted, which eliminates the need to manipulate the equation. In contrast, proportions require setting up the equation correctly and solving for the desired variable, which may be more complex and time-consuming.
In summary, while both conversion factors and proportions can be used to convert measurement units, conversion factors are generally considered easier because they involve direct multiplication by a known ratio, requiring fewer steps and calculations compared to setting up and solving proportions.
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http://www.infoplease.com/encyclopedia/science/common-weights-measures-table.html
http://www.mathsisfun.com/algebra/proportions.html
What do you think?