Calculator Stress Test

Lab Activity 2.8.1 Calculator Stress Test

Introduction.

Math teachers used to tell students that they needed to learn their arithmetic because they wouldn’t always have a calculator in their pocket. But it turns out that those teachers were wrong. However, this doesn’t mean that everyone really understands how to use their calculator, or that every calculator is the same. This lab activity will have you use a number of different types of calculators and try to identify particular quirks that they may have.

Equipment List.

At least two different cellphone calculators
Internet access to use following online calculators:
- (TheOnlineCalculator.com) Basic Calculator
  ¹⁰
  www.theonlinecalculator.com/
- (Online-Calculator.com) Standard Calculator
  ¹¹
  www.online-calculator.com/
- (Desmos.com) Scientific Calculator
  ¹²
  www.desmos.com/scientific/

Procedure.

We are going to investigate the calculators and learn about their individual quirks. You will want to take notes throughout so that you will be able to remember the information you need for the write-up.

Determine the following information about the two cellphone calculators and three online calculators:
- Basic calculator information (cellphone calculators only): Determine the cell phone brand, calculator name, and calculator version. (Note: The calculator might just be called "calculator." The version information might be difficult to find, but it’s there somewhere. You might find the information in the app store.)
- Calculator type: Basic or scientific. (Note: Some calculators allow you to use either mode. If so, indicate this and use scientific mode for the rest of the lab.)
- Execution style: Infix or immediate execution
- Parentheses, square, and square root: Determine whether the calculator allows the use of parentheses, the squaring function, and the square root function.
- Scientific Notation: Determine whether the calculator accepts scientific notation. (Note: If the calculator is infix and has an exponentiation function, then you can use scientific notation. But some calculators will have an E or EE button for scientific notation.)
We will use the calculators to calculate some values. The purpose is to compare the relative difficulty of getting the correct answers. In some cases, you might be able to perform the entire calculation in a single step. But in other cases, you may need to perform multiple separate calculations to get the correct result. Be sure to make note of any challenges you encounter.
- Calculate \(\frac{10}{5+5}\text{.}\) The correct result is 1.
- Calculate \(1 + 2 \cdot 3\text{.}\) The correct result is 7.
- Calculate \(2 + \frac{6}{3} + 3\text{.}\) The correct result is 7.
We will now test some of the limits of the calculators. Perform the following tasks on each calculator.
- Calculate \(1 \div 3\) and count the total number of digits that are displayed (including the leading zero). Then calculate \(1,000,000 \div 3\) and count the number of digits that are displayed. Indicate whether there are more, fewer, or the same number of digits in the display.
- Determine the highest power of 10 that the calculator will accept without giving an error. This is easiest on calculators that have exponentiation or scientific notation. If it does not have these features, it will be helpful to use the "Ans" feature (uses the answer of the last calculation as part of the next calculation) or the memory feature to store large powers of ten. Make a note of the error it gives when it breaks.
- If the calculator has a square root function, determine the maximum number of 9s needed for the calculator to display that \(\sqrt{0.999\ldots9} = 1\text{.}\) (Note: It is possible that for some calculators, it will not display this result even for a large number of 9s. If that happens on one of your calculators, just indicate this.)
We will now engage in some "stress tests" of the calculators. The goal is to see whether we can make the calculator make mistakes. Note that if the instruction says to "calculate" a quantity, it means to have the calculator evaluate the result by pressing the equal sign (or equivalent button).
- Calculate \(1 + 2 \times 3\text{.}\) Do not add parentheses or make other adjustments to force the calculator to get the right answer. We want to see how the calculator interprets this. The correct answer is 7, but some calculators will give 9 as the answer.
- Calculate \(1 \div 3\) and then multiply that result by \(3\text{.}\) The correct answer is 1, but not all calculators will give this result.
- Calculate \(\sqrt{0.999\ldots9}\) with as many 9s are needed to give a result of 1. Then square the result. The correct answer is \(0.999\ldots9\) with as many 9s as you entered when you started. However, some calculators will have rounding error and simply return a value of 1.
- For calculators with a squaring function and a square root function, start with \(0.1\) and square as many times as needed to get a result of 0. Then take the square root. The correct answer is a very small positive one, but some calculators will give 0. For calculators that give a small positive number square twice and take the square root twice to see if it makes a difference. Continue squaring more and more times until it gets stuck at 0.
- For calculators that have parentheses and inline notation (so that fractions appear as \(1 \div 3\) or \(1 / 3 \) instead of \(\frac{1}{3}\)), calculate \(6 \div 2 (1 + 2)\text{.}\) If the calculator does not give an error, indicate what answer it gave. (Note: This calculation is hotly debated on the internet, and it is known that different calculators give different answers. What the "right" answer is and whether there even a "right" answer depends on who you ask.)

Discussion.

Answer the following questions.

Based on your experiences, which calculator would you say is the "best" one? The "worst" one? (Note: It’s possible for multiple calculators to tie for best or worst. This is purely subjective.) What are your reasons for your rankings? Also indicate if there is disagreement within the group about these answers.
Did any of the stress test results surprise you? What about them was surprising?

Conclusion.

It’s a common assumption that everyone knows how to use a calculator. This assumption is true for very basic calculations, but it’s often false when more complex calculations are involved. Was there anything new that you learned about calculators from this activity?

Lab Write-Up Guidance.

Use the following outline to help you write up your lab report completely and correctly.

Title and Header.
What is the title of the lab and who was in the lab group?
Introduction.
In your own words, what was the purpose of the lab activity? This should only take a few sentences for this lab.
Procedure.
This lab has you executing a number of calculations using different calculators. Describe the various calculations that you did.
Results and Data.
You should have one table of information the describes the calculators. Then you should have another set of tables (one table for each calculation) where you indicate which calculators you used and the results of the calculations.
Discussion.
Answer the discussion questions. Be sure that you state the original question and organize it in a way that is easy to follow.
Conclusion.
Write a couple paragraphs about the lab. Did you find anything interesting or surprising? Did you learn anything new about calculators?

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