New answers tagged

1

It depends on the level of the class. I would expect someone who has a recent undergraduate degree in mathematics to have experienced significant figures at at least some point in their life, either in high school or in college. I would also expect common sense to kick in and say that the level of accuracy proposed is unreasonable. But it is reasonable to ...


0

I would say that based on the words of the question, the answer is 35. It is not a distance or measurement of 22 miles between points A & B. It is a journey between locations A & B. Next time you see the guy who scolded you, ask him how one should answer if asked, “What is the numerical value of pi minus e?”


2

It depends I agree with just about everyone that the answer is 35, or perhaps 35.4 (a number I like better, see below). An answer of 35.405598 km is precise to the millimeter. I've ridden horses; they don't work in millimeters. Update: For what it's worth, after all this discussion, I think that the right number is "about 35 and a half" (not 35.5) ...


25

Here's a joke I like to tell when people could use a reminder about precision vs accuracy: A tour guide at Giza was explaining how the Pyramids were 4507 years old. Someone in the crowd asked: "That's oddly specific. How do we know this?" "Well. I was told they were 4500 years old when I started working here 7 years ago." I'm not sure ...


2

You're both right, depending on the domain of discourse and the rules of engagement. In pure math, the traditional expectation is that the numbers given are exact unless stated otherwise, and answers are also to be exact unless stated otherwise. So when the mathematician read "22 miles," he's using a tradition that means "exactly 22 miles.&...


17

Just to play the devil's teacher's advocate here: one can make a point that rounding should be generally avoided but measurement uncertainty instead be expressed explicitly. Specifically, rounding errors should always be much smaller than measurement errors. Now, if you have a figure of 22 miles, I'd interpret this as $(22\pm0.5)\mathrm{mi} = (35.4\pm0.8)\...


2

IF the horse ride were 22.00000000 miles then the other person would be right. Else if it were 22 miles then you should round the answer to zero decimal places. Some people are illogically pedantic without any rational reason for what they promulgate.


9

When I was in school, I once got an answer marked as error for having too many digits. IIRC it was in trigonometry and I had just written down as many digits as the calculator displayed. (I was able to discuss it away, but was told to avoid unreasonable amounts of digits in the future) That was in the 1990s in continental Europe, but I think it is still good ...


38

The product of two numbers should be given with as many significant digits as the least precise of the numbers multiplied (see https://www.nku.edu/~intsci/sci110/worksheets/rules_for_significant_figures.html). 1.60934 km/mile has six significant digits (or, if a mile is defined to be an exact number of km, then the conversion factor has an infinite number of ...


15

When a tutoring student asks me about rounding, I tell them that absent specific instructions from a teacher, common sense should apply. For a conversion, 22 miles isn’t 22.0000 miles, there’s the assumption it’s been rounded. You can’t convert and find yourself with 6 digits of accuracy beyond the decimal. As you note, there’s a number of digits that result ...


42

You're right. The random, anonymous person you met online is not competent. This is basic mathematical literacy, as taught in every freshman chemistry and physics class.


4

“ I know it has a lot of relations with the mathematics, with the logic, many applications in computer science, game theory and so on.“ Do you know these specific relationships and are you prepared to introduce/explain these things in the context of the game? If so, that sounds like it should take quite a bit of preparation on your part to teach a complex ...


7

It's a bad idea. (1) It's not that special. He can get a game from chess very easily from anyone. An individual session with you is not high value, not best use of time. (2) It will raise hackles. I would suggest instead introducing some recreations that are less familiar instead. Playing Hex for instance is an idea. The value is much higher than chess, ...


4

I am quite surprised by the suggestion (and apparent consensus?) that kites and rhombi are not very important for high school geometry. Here are three entirely different arguments for why they should, in fact, play a central role in the curriculum. Argument 1: Understanding hierarchical relationships. One of the goals of secondary Geometry is to help ...


1

It would be hard to say what you could get rid of without knowing what is on your state test. In my state (NY), they push quads quite a bit. I'll grant you that kites aren't interesting or important, but rhombuses are both. One of the usual capstone problems is being given the coordinates of four points and demonstrating that the quadrilateral formed from ...


1

OP: "I am fairly sure that rhombuses and kites are pretty useless." Understanding parallelograms and rhombi is quite useful in pop-up card design:       Constructed by Ian Agol. Twitter link; "inspired by @divbyzero's tweet." 19Dec2020.


1

The observation that a rhombus's diagonals bisect its internal angles gives rise to an efficient method to find an angle bisector. Here, a British national-exam question hints this method to the candidate:


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