I was explaining to Dion yesterday how unthinking students can be in applying rules for significant figures. They try to memorise and apply rules of thumb instead of reason. Many will tell you that "Zeroes after the decimal point are significant; therefore, 0.00182 m has five significant digits." I suppose it would have eight if written in km. 0.00000182 km. No consideration of certainty or precision is to be found here. Dion's response was that they should just be using scientific notation, i.e., 1.82 X 10^-3 m. Indeed, scientific notation is superior to standard notation in this respect. Unfortunately, in everyday life and definitely in most Physics textbooks, most values are stated in standard notation.
This reminded us of an incident I meant to blog. At Chinese New Year with Dion's extended family, we played the name game. One clue provoked later discussion on the relative merits of improper versus mixed fractions. Most of us prefer improper fractions. Mixed fractions are computationally inelegant. We're snobs with engineering, science, accounting, ... degrees. However, as a math teacher, I felt obliged to point out that in everyday life, no one uses improper fractions. Would I say that I'm 15/2 months pregnant? Of course not. The paper is 17/2 by 11 inches? equally stupid.
Dion's cousin, who is in Grade 9, was in the game for the first time rather than just time keeping and recording scores. He had put in one clue then later picked it up himself. He was able to get his teammates to say, "improper fraction," but despite clear appeals to the equivalence of another form, they could not come up with "mixed fraction." After some time and several tries, he exasperatedly retorted, "Don't you guys know math?". Pwned.
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2 comments:
Good thing you're not an English teacher... "Pwned"?
Significant figures seem sort of arbitrary... isn't there virtually the same level of precision in measurement of 0.999 and 1.000, yet the have a different number of significant figures (okay, some people say that division is at 1.999 and 2.000, but it's the same either way). It should all be done with error calculations! I wouldn't want to do all the calculations that way, but it is more correct.
.00182 metres vs .00000182 km. What is the difference. In actual terms, there is no difference since they both refer to same length. However if we look more closely at the unit, it becomes clear that in the first instance, one is looking at measuring with a fair short measuring instrument and its precision is 1 part in 10000, but the other is long or large measuring instrument with a precision of 1 part in 10,000,000.
If I may use an analogy, if you measure in terms of light years, you are impling a very large unit, and resolution to the centimeter level with such an instrument would be incredibly accurate. (maybe??)
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