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22 votes

What are some simple problems that calculators get wrong?

The first sentence of the question is "A frequent issue with students is their uncritical over-reliance on computation devices," hence my answer is in the spirit of presenting something ...
Xander Henderson's user avatar
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14 votes

What are some simple problems that calculators get wrong?

The last time I taught introductory numerical analysis, my first slide was this print from excel: If you want another example: These calculations are clearly easy and wrong, as required. Remark 1: ...
Pedro's user avatar
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13 votes

What are some simple problems that calculators get wrong?

Evaluate $L=\lim\limits_{x\to 0^+}(\sin x)(\ln x)^{100}$. Letting $f(x)=(\sin x)(\ln x)^{100}$, students might use their calculators to find that: $f(0.1)\approx 1.66\times 10^{35}$ $f(0.01)\approx 2....
Dan's user avatar
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11 votes

What are some simple problems that calculators get wrong?

The easiest example off the top of my head is evaluating $(9^n)^{1/n}$ for a ridiculously large value of $n,$ large enough to have the calculator throw an overflow error. Something like $(9^{9^9})^{(1/...
Justin Skycak's user avatar
10 votes

Loaning students calculators during exams

To summarize what I arrived at, based on the top answer on my prior parallel question on SE Academia, OP's #2 is the way to go -- keep a small supply of calculators on hand, but assess a usage penalty ...
Daniel R. Collins's user avatar
8 votes

What are some simple problems that calculators get wrong?

Ask a TI-89 to evaluate $\sin(n \pi)$ for different integers $n$, and you'll start out fine (when $n = 0, 1, 2, 3$), but starting with $n = 4$, you'll get values like $-2 E -13$. Or there's $8^{8^8}$ ...
Nick C's user avatar
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7 votes

What are some simple problems that calculators get wrong?

In a rather different vein, calculators can be correct in a numerical sense but miss an optimal solution method. In this answer two such cases are described, and I refer the reader to the above link ...
Oscar Lanzi's user avatar
7 votes

What are some simple problems that calculators get wrong?

The easiest of all:$$\frac{1}{3} \cdot 3$$ :-) You can also go for large squares, something like: $$\frac{123456789^2 - 123456788^2}{123456789 + 123456788}$$ => for a human, this is just $\frac{a^2-...
Dominique's user avatar
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6 votes

What are some simple problems that calculators get wrong?

Occasionally I ask my students true-false questions of the following form: T/F? $1/3 = 0.333333333$ T/F? $\pi = 3.141592654$ They usually get these right as a group, but I think it's good to check ...
Daniel R. Collins's user avatar
6 votes

What are some simple problems that calculators get wrong?

Combinatorics might be a good place to look. A very basic example: given 200 items, how many ways are there to pick 1 item? Using the permutation formula involves calculating $200!/199!$, which not ...
BenM's user avatar
  • 177
5 votes

What are some simple problems that calculators get wrong?

Computers are quite bad at drawing curves with self-intersections. Examples below are made with Maple 13 (a quite dated version). The graph of $x^2+y^2=3xy$ looks particularly strange. We can get a ...
Taladris's user avatar
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5 votes

What are some simple problems that calculators get wrong?

Many cheap calculators ignore operator precedence. Type 1+2*3 on a good one and you'll get 7, do it on a cheap one and you get <...
Guntram Blohm's user avatar
4 votes

Loaning students calculators during exams

My intuition is that further penalizing already disengaged students will likely lead them to become even less engaged. It also sounds like some of these students might not know how to use scientific ...
TomKern's user avatar
  • 4,425
4 votes

What are some simple problems that calculators get wrong?

Some scientific calculators will round certain rational numbers to rational multiples of pi. For example, $\frac{11^6}{13} \approx \frac{156158413}{3600} \cdot \pi$. They may be assuming that the user ...
justforplaylists's user avatar
4 votes

What are some simple problems that calculators get wrong?

Continuing in the vein of "The calculator is right, but the interpretation by the user is wrong" I add a class of problems of the form $$\lim_{x \to \infty} \frac{p(\log(x))}{q(\log(x))}$$ ...
Opal E's user avatar
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4 votes

What are some simple problems that calculators get wrong?

Since I was asked to post a comment of mine as an answer to my own question, here is a refined version: Problem: Evaluate $$\text{log}_{10}(10^{\frac{1}{10^{17}}})^{-1}.$$ By hand, this easily ...
Carl's user avatar
  • 199
4 votes

What are some simple problems that calculators get wrong?

Here is a simple example. $ \def\lfrac#1#2{{\large\frac{#1}{#2}}} $   $\color{green}{\Big( 99 · \big( 100·\sum_{k=0}^{10} (-\lfrac1{99})^k-99 \big)^\lfrac1{10} - 1 \Big)^\lfrac1{9} = 0}$. Windows Calc ...
user21820's user avatar
  • 2,649
3 votes

What are some simple problems that calculators get wrong?

Type the following into Wolfram Alpha: integrate sin(pi x)/(x(1-x)) from x = 0 to x = 1 Half the time Wolfram Alpha gives a correct estimate and half the time it says the integral is $0$, even when ...
KCd's user avatar
  • 3,516
3 votes

What are some simple problems that calculators get wrong?

An example discussed in math.se in the past is this: $-4^2$ is interpreted by all mathematicians as $-(4^2) = -16$. But some calculators (and even some elementary-school teachers) will interpret it ...
Gerald Edgar's user avatar
  • 7,607
3 votes

Loaning students calculators during exams

Allow the students to use Desmos Test Mode. The app allows students to lock a phone or other android/iOS device in single-app mode and use the Desmos graphing calculator that we know and love in an ...
Chris Cunningham's user avatar
2 votes

Loaning students calculators during exams

In my opinion, all of your decisions should be based on the following question: What is the pedagogical goal? In my classes, I generally try to focus on the mathematics and on basic (basic) "how ...
Xander Henderson's user avatar
  • 8,225
2 votes

What are some simple problems that calculators get wrong?

A simple example, due to Velvel Kahan (UCB), is $$(((4/3)-1)*3)-1$$ is usually not zero (and should not be zero on IEEE-754 compliant floating-point systems; the HP 35s yields $-1{\rm e}{-}11$). Note ...
user1815's user avatar
  • 5,595
2 votes

What are some simple problems that calculators get wrong?

Division by 0 This is pushing the definition of "easily be solved by hand" since the "solution" is to see that it's indeterminate. Which calculators have this issue? When you try 1/...
SkySpiral7's user avatar
1 vote

What are some simple problems that calculators get wrong?

Here's an expression that evaluates to something very clearly inaccurate on most calculators: $$\frac{1}{\left(\left(\frac{4}{3}\right)-1\right)\cdot 3-1 + 10^{-20}}$$ Most floating point calculators ...
ksimplex's user avatar
  • 111
1 vote

What are some simple problems that calculators get wrong?

Why not problems like $(-1)^z=2$, or $i^z=3$? Even better if you ask for all solutions in their exact form. ($i$ in this case being defined as $\sqrt{-1}$) For both of these examples:$$(-1)^z=2\\\text{...
CrSb0001's user avatar
  • 295
1 vote

Why are calculators not allowed in post-secondary exams?

I administer individual math assessments to students. I think students need to learn to understand basic math concepts and apply them to every day situations. The best way to do that is to learn basic ...
Ron's user avatar
  • 11

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