Before we begin, always remember: Astronomers Love to Approximate.

Math: You've all used and perhaps rely on calculators to do most, if not, all your calculations. In this class, I'm not going to outright ban calculators, but I probably should :) Instead, I'm going to strongly recommend that you get into the habit of using scientific notation and approximation instead of your calculator. Scientific notation and approximation will help you calculate quickly and without any need for calculators. Think about it for a moment, when using scientific notation all your calculations are reduced to just adding and multiplying integers between 0 and 9, that's it. Once you get an approximate answer that looks to be in the ballpark of what you would reasonably expect, you can then either box that up, or proceed with using a calculator to check your work and see that your calculator agrees with your approximation. You are more powerful than the calculator.

Units: I can not stress what I'm about to say enough -- Units are the most important part of your calculation! I don't mean, it's important that they are present at the end of the calculation. I mean, they should be present in every single step of your calculation. If you have a line without Units, it's wrong. I will take points off. When I was student, I used to think Units were a pain and could be easily ignored while I worked on the numbers, and just put the Units I expect in at the end. This was a terrible strategy and resulted in many errors and confusion. It was only when I started with the Units, and did the Units Algebra on every step that I started to get right answers more often, and also understood better what was happening. I'm capitalizing Units because they are so important in this class they deserve to be capitalized.

So, in summary, every calculation should follow the following steps:

1. Show all your work. There's no shame in showing ever single step of your work.

2. Be neat, skip lines. Each individual has their own aesthetic preferences, but from experience I often see students with neat work getting right answers more often than students whose work is a mess. One tip for being neat, have all your equal or approximation signs line up vertically, skip lines, give yourself plenty of space.

3. Units (unless you're doing a dimensionless problem) should be present in every line of the calculation.

4. Scientific notation should always be used for numbers larger than ten.

5. Approximate! As long as you're reasonable with your approximations, your resulting answer should also be reasonable. In this class I will give you the same credit for a correct approximate answer as I would for an answer calculated to eight significant figures.

6. Organize. Once you've included all your Units and scientific notation, group all the numbers to the left and all the Units to the right. This will help you focus on doing algebra with the numbers and the Units Algebra. If you keep everything jumbled up, you run the risk of making mistakes.

7. Reflect. Once you arrive at an answer, think for a moment 'Does this answer make sense?' This brief moment of reflection will often alert you if you truly are on the right path, or perhaps made a mistake. If something seems much smaller or larger than it should, it's probably an error in one of the exponents. By having all your work neatly written out above, you can then easily track back and hopefully find the mistake.

While working through the new chapters, try applying all these steps to the examples you encounter. You will see a vast improvement in your calculation skills. If not, come to office hours! I'll be standing by and ready to help.