This a recap of my process to doublechecking math that I perform about the real world.
First and most importantly, math should be solved algebraically first, and only then computed using a calculator. Start by defining exactly what value you’re looking for along with what units you want it to be in. Then start collecting and writing out your input numbers with units as lettered variables. You can add to this list later if you realize you need another variable, but always write it out. This allows you to return to your notes, if you want to revisit some result.
Importantly, you can invent units on the fly. I once computed how many custom six-sided dice a UV printing machine could handle in an hour. For this, I invented two new units: die, and side. This gave me compound units like side/hour, die/hour. This also allowed me to define a conversion rate for these two values: 6 side/die.
The question I wanted to answer was how many dice/hour a machine could handle. I found that the machines could handle, let’s say, . I then found the size of a 14mm die side, which gave me the conversion rate . I used the conversion to make this calculation, which brings me to a second big point: don’t treat denominations of units as the same unit. Meters and Millimeters should not be treated like different sizes of the same unit, or else you risk making a mistake. The only way to get Meters from Millimeters is to use a conversion rate, just like converting dice to sides.
To reiterate and expand upon the rules for units (which includes invented units):
This was my process for doublechecking math in my undergraduate physics classes.
There are 5 things you should check after performing math in physics:
This process starts with checking the precise question. Find all question marks ? in the problem and identify the following things about the requested answer:
You then check your