Can someone explain to me in there own words How is using a conversion factor different than using proportions to convert measurement units and which one is easy because i don't understand
You can always multiply by 1 without changing things.
A conversion factor is just a way of writing 1 so that units cancel as desired.
Suppose you want to convert lbs to kg.
You know that
2.2lb = 1kg
So,
2.2lb/1kg = 1
1kg/2.2lb = 1
So, if you want to convert kg to lbs, you can do (staring with 5 lbs)
5lb * 1kg/2.2lb = 5/2.2 kg = 2.27kg
because the lb units cancel.
Using these conversion factors is a good way to keep track of what to use to multiply or divide. Always set it up so that the units you don't want cancel out, leaving the target units.
Okay thanks i like how you broke it down
Of course! I'll do my best to explain the difference between using a conversion factor and using proportions to convert measurement units.
When it comes to converting measurement units, both conversion factors and proportions can be used. Let's start with proportions.
Proportions involve setting up an equation where two ratios are equal to each other. For example, if you want to convert 2 meters to centimeters, you would set up a proportion like this:
2 meters / 1 = x centimeters / 100
Here, we know that 1 meter is equal to 100 centimeters, so we set up the proportion accordingly. By cross-multiplying and solving for x, you can find that 2 meters is equal to 200 centimeters.
On the other hand, using conversion factors is slightly different. A conversion factor is a ratio that represents the relationship between the original unit and the desired unit of measurement. It is derived from scientific or common knowledge.
Continuing with the same example, the conversion factor for converting meters to centimeters is known to be 100 cm / 1 m. To convert 2 meters to centimeters using a conversion factor, you would multiply 2 meters by the conversion factor:
2 meters * (100 cm / 1 m) = 200 centimeters
As you can see, using a conversion factor eliminates the need to set up a proportion. You simply multiply the original measurement by the conversion factor, ensuring the units cancel out correctly.
Now, as for which method is easier, it often depends on personal preference and the specific scenario. Some people might find proportions more intuitive, while others find conversion factors to be simpler and more direct. It may vary from person to person.
I hope this explanation helps clarify the difference between using conversion factors and proportions for unit conversions. If you have any more questions, feel free to ask!