## Topic F. Using a Calculator

### Objectives:

- Understand that different calculators require a somewhat different order of entering numbers and operations. Be able to use the correct order on YOUR calculator, and recognize which other calculators require a different order.
- Perform basic operations and square root
- Use exponents—not just squares and cubes
- Use the constant pi.
- Learn the difference between entering a negative number and the operation of subtraction.
- Learn to put in parentheses when needed.
- Read the output when it includes scientific notation.
- When and how much should you round the results?
- Checking your work with a calculator. (Estimation)

### Discussion: Types of calculators

Generally speaking, the various brands of calculators all work in pretty similar ways, so the differences are in the type of calculator, not the brand.

We might think of four categories of calculators typically used by students:

- Basic calculators. These add, subtract, multiply, divide, and a few other things. They cost $2 to $8.
- Scientific calculators with a one-line display. These cost $5 to $15.
- Scientific calculators with a two-line display. These cost $8 to $20.
- Graphing calculators. These cost $40 to $150.

For these materials, the basic calculators don’t have enough capability and the graphing calculators have much more capability than needed and are more expensive than needed. Either of the two types of scientific calculators is acceptable. However, we enter various operations into them in different ways, so you’ll find it easier to pick one type and always use it. If you already have a scientific calculator, you can use it for this course. Most students find that they prefer a calculator with a two-line display. Those enable you to see what you entered and the result at the same time, which is not possible on the one-line-display calculators.

**Example 1**. Perform basic operations and square root.

Try all of these problems on your calculator to make sure that you understand what to enter to obtain the correct answer:

- [latex]3+4[/latex]
- [latex]7-12[/latex]
- [latex]12\div4[/latex]
- [latex]8\cdot3[/latex]
- [latex]\sqrt{36}[/latex]

**Solution**: You know how to do all of these operations without a calculator. Do them and then make sure you can get the same answer with your calculator.

**The order in which you enter the numbers and operations is different on different calculators**. Practice with the calculator you will use in this course. Make a note in the margin here about anything you must remember in order to enter these into your calculator.** **

**Example 2**. Use exponents—not just squares and cubes.

- Find [latex]{{2}^{4}}[/latex]
- Find [latex]{{3}^{0.7}}[/latex]
- Find [latex]\sqrt[5]{32}={{32}^{{}^{1}\!\!\diagup\!\!{}_{5}\;}}[/latex]
- Find [latex]\sqrt[6]{79}={{79}^{{}^{1}\!\!\diagup\!\!{}_{6}\;}}[/latex]

**Solution**: Most scientific calculators have a square and a cube key (powers of 2 and 3.) But we will need to compute other powers. The exponent key on most calculators is denoted by one of these symbols: [latex]{{y}^{x}}[/latex], [latex]{{x}^{y}}[/latex], or ^.

- By hand (or in your head) find that [latex]{{2}^{4}}=16[/latex].

Find the exponent key on your calculator and make sure that you can use it correctly.

Practice by evaluating [latex]{{2}^{4}}[/latex]. - Then use the same method to find [latex]{{3}^{0.7}}[/latex]. (That answer should be 2.157669.)
- You’ll need parentheses around the fraction in the exponent. [latex]\sqrt[5]{32}={{32}^{{}^{1}\!\!\diagup\!\!{}_{5}\;}}=2[/latex]
- Again, use parentheses around the fraction in the exponent. [latex]\sqrt[6]{79}={{79}^{{}^{1}\!\!\diagup\!\!{}_{6}\;}}=2.071434[/latex]

**Example 3**. Use the constant [latex]\pi[/latex].

- Find [latex]\pi[/latex].
- b. Find [latex]2\pi[/latex]
- c. Evaluate the area of a circle with radius 2: [latex]A=\pi{{r}^{2}}[/latex].

**Solution**:

- This is the Greek letter “pi” which denotes a number which is the ratio of the circumference of a circle to its diameter and is approximately 3.14. It is used in many geometry formulas involving round objects. Often we need to use it to a greater accuracy than two decimal places. Most scientific calculators have a key for . Have you noticed that your scientific calculator has two different values for most keys? One, called the main value, is labeled on the key itself and the other, called the secondary value, is usually labeled right above it. To get that secondary value, you must press a specific other key on the calculator first. That is the “2nd” key or maybe “Shift” or “Inv”. Almost always it is the top left key of the calculator keyboard. On many calculators, the [latex]\pi[/latex] key is a secondary key value, so you’ll need to punch that top left key first. When you find that key, you’ll be able to see that [latex]\pi=3.14159….[/latex]. The different calculators have different numbers of decimal places.
- To find [latex]2\pi[/latex]on your calculator, you must learn to use multiplication and the second key in the correct order. You can check your work, of course, by multiplying 2 times 3.14159… by hand to see if your calculator is giving you the correct answer.
- Notice how to enter these into your calculator so that the operations are done correctly. On one-line-display calculators, you may need to square the radius before multiplying by [latex]\pi[/latex].

[latex]A=\pi{{r}^{2}}=\pi\cdot{{2}^{2}}=\text{12.56637061}[/latex]