Dimensional+Analysis

In physics, you sometimes have to convert units. For example, if you are calculating something in grams, you might want to convert it into kilograms for an equation. Other times, the numbers are in a whole different system, and you want to know how much the number is in pounds. This is where dimensional analysis comes in. In this way, you can easily convert any number from one unit of measurement to another. With the method that I am about to show you, you can do this with the minimum room for error, and it is quick, too.

Here is what you would do if you were converting 54 yards to meters:


 * Step 1: **

First, you have to put the number in a fraction form, like this…

//__ 54 yards __// // 1 //


 * Step 2: **

Write down what unit that is trying to be reached in the end. Then, you should see what different conversions can be made to get from the starting unit to the final one. In this problem, you should go from yards to feet to inches to centimeters to meters.


 * Step 3: **

Next, you should make the first conversion, yards to feet. Since you are starting with a fraction, you want to multiply it by another fraction to cancel out the yards and leave you with feet. One yard equals three feet, so…

//__ 54 yards __////__ 3 feet __// // 1 * 1 yard //

Now, if you multiply the equation out as it is, you would get 162 feet, because the yards cancel out.


 * Step 4: **

After that, write out all the other conversions after your equation…

//__ 54 yards __////__ 3 feet __////__ 12 inches __////__ 2.54 cm __////__ 1 meter __// // 1 * 1 yard * 1 foot * 1 inch * 100 cm //

Again, all the units are cancelled out except for the meters, because that is what we are converting to.


 * Step 5: **

Finally, multiply everything together…

//__ 54 yards __////__ 3 feet __////__ 12 inches __////__ 2.54 cm __////__ 1 meter __//// = ////__ 4937.76 meters __//// = 49.3776 meters // // 1 * 1 yard * 1 foot * 1 inch * 100 cm 100 //

** *When you are doing dimensional analysis, and you come across units such as 50in² to cm², you must multiply the units twice. **
Example: __50in²__ * __2.54cm__ * __2.54cm__ = 322.58cm² 1 * 1in * 1in

The reason this is done is there are not one, but two dimensions for inches, so you need to multiply them twice so the units cancel out.

Now you’re done!