Converting Units
Converting between units can be done through the use of conversion factors or specific conversion formulas.
Learning Objective

Apply factorlabel method for converting units
Key Points
 Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.
 The factorlabel method is the sequential application of conversion factors expressed as fractions in which units appearing in both the numerator and denominator can be cancelled out, leaving only the desired set of units.
 For conversions that have a difference factor, specific conversion formulas should be used.
Term

conversion
a change between different units of measurement for the same quantity.
Full Text
Translating Systems of Measurement
It is often necessary to convert from one type of unit to another. Conversion of units is the conversion of different units of measurement for the same quantity, typically using conversion factors. For example, if you are reading a European cookbook, some quantities may be expressed in units of liters; if you're cooking in the US in a standard kitchen with standard tools, you will need to convert those measurements to cups. Or, perhaps you are reading walking directions from one location to another and you are interested in how many miles you will be walking. In this case, you will need to convert units of feet to miles. This is a bit like translating a substitution code, using a formula that helps you understand what one measure means in terms of another system.
Conversion Methods
There are several ways to approach doing conversions. One commonly used method is known as the Factorlabel method for converting units, or the "railroad method. "
The factorlabel method is the sequential application of conversion factors expressed as fractions and arranged so that any dimensional unit appearing in both the numerator and denominator of any of the fractions can be cancelled out until only the desired set of dimensional units is obtained. For example, 10 miles per hour can be converted to meters per second by using a sequence of conversion factors.
Each conversion factor is equivalent to the value of one. For example, starting with 1 mile = 1609 meters and dividing both sides of the equation by 1 mile yields 1 mile / 1 mile = 1609 meters / 1 mile, which when simplified yields 1 = 1609 meters / 1 mile. Physically crossing out the units that cancel each other out will also help visualize what's left over .
Converting 1 year into seconds using the FactorLabel Method
Physically crossing out units that cancel out helps visualize the "leftover" unit(s).
So, when the units mile and hour are cancelled out and the arithmetic is done, 10 miles per hour converts to 4.47 meters per second.
A limitation of the factorlabel method is that it can only convert between units that have a constant ratio that can be multiplied, or a multiplication factor. This method cannot be used between units that have a displacement, or difference factor. An example is the conversion between degrees Celsius and kelvins, or between Celsius and Fahrenheit. For these, it is best to use the specific conversion formulas.
For example, if you are planning a trip abroad in Spain and the weather forecast predicts the weather to be mostly cloudy and 16°C, you may want to convert the temperature into °F, a unit that you are more comfortable interpreting. In order to do this, you would need to know the conversion formula from Celsius to Fahrenheit. This formula is: [°F] = [°C] × ^{9}⁄_{5} + 32.
[°F] = (16 × ^{9}⁄_{5})+ 32
[°F] = 28.8 + 32
[°F] = 60.8
So you would then know that 16°C is equivalent to 60.8°F and be able to pack the right type of clothing to be comfortable.
Key Term Reference
 application
 Appears in these related concepts: Introduction to Elementary operations and Gaussian Elimination, Physics and Other Fields, and XRay Imaging and CT Scans
 displacement
 Appears in these related concepts: Position, Displacement, Velocity, and Acceleration as Vectors, Reference Frames and Displacement, and Introduction to Human Language
 equation
 Appears in these related concepts: Equations and Inequalities, Graphs of Equations as Graphs of Solutions, and What is an Equation?
 kelvin
 Appears in these related concepts: Celsius Scale, Temperature, and Speed of Sound
Sources
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