the form of the conversion factor that is used is the one in which the unit of the_ is in the denominator
It's tough to fill in the blank with so little information; however, the unit you start with goes in the denominator and the unit you want to keep goes in the numerator. The word initial may fit the blank.
When using conversion factors, we can express them in different forms depending on the desired outcome. In this case, you mentioned that the unit of measurement should be in the denominator.
To understand this, let's start with the basics. A conversion factor is a ratio between two different units of measurement that allows us to convert between them. It is generally derived from the relationship between the units and is expressed as a fraction.
For example, let's say we want to convert units of length from inches to centimeters. The conversion factor between inches and centimeters is 2.54 cm/inch. This means that for every 1 inch, there are 2.54 centimeters.
To convert from inches to centimeters, we can set up a conversion factor equation:
Length in centimeters = Length in inches × Conversion factor (cm/inch)
In this case, the unit "inch" is in the denominator of the conversion factor.
So, it follows that for the conversion factor to have the unit of measurement in the denominator, we need to ensure that the desired unit we want to convert to is in the numerator of the conversion factor. This allows us to cancel out the initial unit and achieve the desired conversion.
Here's another example: Let's convert from hours to minutes. The conversion factor between hours and minutes is 60 min/hour. To convert 3 hours to minutes, we can set up the equation:
Time in minutes = Time in hours × Conversion factor (min/hour)
Here, the unit "hour" is in the denominator of the conversion factor, and the unit "minute" is in the numerator.
By using the appropriate form of the conversion factor, with the desired unit in the denominator, we can correctly convert between different units of measurement.