It is interesting how the numbers we use in a math class are different from the numbers we encounter in real life. Over the summer, we were working with calculating the sales tax on a jacket that cost $60. In real life, nothing costs $60. The calculation for sales taxes is identical for something that is $59.99 or $60. I wonder if we used more realistic numbers, if students would be terrified by the slightly more complex calculations or it would help them feel more empowered in the real world.

XKCD Original (I cropped to 'keep it rated G') |

Now, just for a bit of math before I go. What does 21/29 actually look like? Well, I started doing the long division to figure out what it was as a repeating decimal. After I got the 11th digit after the decimal point, without seeing a pattern, I stopped. I looked on my calculator (which only goes to 9 digits after the decimal point) to double-check my work. I was right, I still had to wait on the pattern. I used Wolfram to get a solution...

0.7241379310344827586206896551 (repeating)

It goes for 28 digits before it starts to repeat! It got me thinking: I wonder what two-digit denominator would lead to the longest period/repeating part of a decimal. I would ask one of my professors, but I am afraid he would put the question on our next test. Back to math homework. Good night inter-web.

That is an interesting question you pose Greg. As teachers, we tend to simplify and problems to make it easier on students. Not once did I ever think that doing so would be a disservice to the students. I think normally the students would freak out but why is that? I would say it is because they have never learned how to approximate since teachers do that step for them.

ReplyDeleteI don't know if I can say that I shouldn't simplify for physics. Physics is too complicated to not simply.

I was about to work on your challenge problem at the end when I noticed I did not have enough information. Are we using 21 as the numerator and changing the denominator to any two digit number? If so, I guessed that using prime numbers would be the most appropriate. So 21/97 has a period 96. That's gotta be close right?