Thank you, Ed. This is an interesting way to think about it. Here is how part of my chart looks right now and I have some accompanying text explaining what I did and why I have the fifth column:
-------- SPEED SKATING Men's year time time in seconds speed in meters/sec 1924 2:20.8 140.8 10.653409 = 10.65 1960 2:10.4 130.4 11.503067 = 11.50 1980 1:55.44 115.44 12.993762 = 12.994 1998 1:47.87 107.87 13.905627 = 13.906 --------
Would you change any of it?
Also, at what age would you explain things this way? What kinds of problems would you use with children so that they would start to understand this? How are teachers teaching about "significant digits" in elementary and middle school?
>I missed Ron's reply and that of others, but I have always thought >about significant digits in a 'statistical' way. So (hopefully my >arithmetic holds up - smile), in that case assume you have 140.8 + x >(where x (in magnitude less than .05 second)- a random 'error' - is >in plus or minus hundredths of a second). Assuming, by way of >example, the distance is precisely known, your answer is 1500/(140.8 >+ x) meters/second. Employing the limits on x suggests that your >answer is roughly in the range 10.650 meters/second to 10.657 >meters/second and 10.65 meters/second seems an appropriate estimate. >If one assumes that that the distance is measured to the nearest >meter (I would assume the accuracy is better than that?) - this opens >the range of variability up a little more - from about 10.643 to >10.664 so 10.65 more or less works. > Oh, I have always thought that rounding off sort of misses the >point (smile). So in the first case I might be inclined to say it is >roughly 10.653 meters/second with an error of +- .004 meters/second. > >Ed Wall
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