\(\def \u#1{\,\mathrm{#1}}\) \(\def \abs#1{\left|#1\right|}\) \(\def \ast{*}\) \(\def \deg{^{\circ}}\) \(\def \ten#1{\times 10^{#1}}\) \(\def \redcancel#1{{\color{red}\cancel{#1}}}\) \(\def \BLUE#1{{\color{blue} #1}}\) \(\def \RED#1{{\color{red} #1}}\) \(\def \PURPLE#1{{\color{purple} #1}}\) \(\def \th#1,#2{#1,\!#2}\) \(\def \lshift#1#2{\underset{\Leftarrow\atop{#2}}#1}}\) \(\def \rshift#1#2{\underset{\Rightarrow\atop{#2}}#1}}\) \(\def \dotspot{{\color{lightgray}{\circ}}}\)
Appendix A: Miscellany
8.

Using Your Calculator

Everyone's calculate is a little different, and I can't give you a full tutorial for yours, but there are a few things you should learn how to do on your calculator, and a few warnings about common mistakes

Try entering the following equations, and see if you get the right answer.

1. What is $4\over 2\times 10^2$?

Answer: 0.02.

If you got 200, then... you probably entered 4$\div$2$\times$10^2. Looks right, but the calculator will do the division before the multiplication, like this $${4\over 2\times 10^2}=(4\div 2)\times 10^2 = 2\times 10^2 = 200$$ Instead of using $\times$10^, you should look for a button like EXP or EE, and you would enter this number as 4$\div$2EE2. The calculator will do the EE before the division (it has a higher priority), which is what you expect.

There is also a common-sense check you can do here: when the denominator is bigger than the numerator, as it clearly is here, then the fraction must be small (less than 1).

2. What is $10^3$?

Answer: 1000

If you got 10,000, then... you may have entered 10EE3. But this is really $10\times 10^3$. If you want to write $10^3$ in scientific notation, you would write it as $1\times 10^3$, and type it as 1EE3.

3. What is $\sin 90^\circ$?

Answer: 1

If you got 0.894, then... your calculator is in radian mode. You should always double-check your calculator's mode when using trigonometric functions, because we will use both degrees and radians in this class (though usually not in the same chapter). We talk more about both in Degrees and Radians. Values in degrees will always have the $^\circ$ symbol after them. Radian values often (but not always) have a $\pi$ in them somewhere. If you're not sure what mode a calculator is in, $\sin 90$ will tell you.

4. What is $2+4\over 1+2$?

Answer: 2

If you get 8, then... you probably entered 2+4$\div$1+2. Because division is a higher priority than addition, your calculator does the division first: $$2+4\div 1+2 = 2 + (4\div 1)+2 = 2+4+2=8$$ Your calculator probably has parentheses buttons (); if so, then you can type this as (2+4)$\div$(1+2).

(The difference between $a\div b$ and $a\over b$ is that the latter has implied parentheses in it: you always evaluate the numerator and the denominator separately. We don't even think about this in real life very often, but calculators don't have that luxury.)