This class, we learned all about dimensional analysis. Dimensional analysis is a problem-solving method that utilizes the fact that any number or expression can be multiplied by one without changing it's value. Just as we convert between currencies or units of length in our daily lives, it is necessary to convert between units in chemistry. Dimensional analysis has 4 steps:
- Identify the units you want to end up with
- Find the conversion factors
- Place the units in their appropriate places
- Cancel out the units
For example, if we wanted to find out how many centimetres are in 6.00 inches, we would do the following:
We know that we want to find out the number of centimetres in 6.00 in. Therefore, the unit that we must end up with is cm. We must also find the conversion factor between the units:
With this information, we can solve the equation, like so:
As you can tell from the above equation, significant digits matter in dimensional analysis. Look at our previous posts for a review of significant digits.
In the next example, we try to figure out the number of seconds in 2 years:
Our answer must be in seconds. We know that there are 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day, and 365 days in a year. Our next job is to place the units in their appropriate places, multiply/divide, cancel out the units, and give the final answer. Here's the full equation:
Dimensional analysis can only be used on units that are related. For example, it's impossible to convert a unit of time to a unit of mass.
Here's a helpful video that explains dimensional analysis from the ground up:
Posted by Michael.
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