You choose the number of useful digits by knowledge of the situation. A
person who is properly taught how to apply the rules of significant digits
knows how many digits apply. A number left in fractional form is not an
answer. If I have a number like 2/3, what does that mean if I'm trying to
build something with it?
Even if you have a number such as 2/3, you still have to assign a level of
accuracy to it. There is no way you can make something exactly 2/3 of
something. You are always going to have to state a plus/minus something
else.
----- Original Message -----
From: "Philip S Hall" <[EMAIL PROTECTED]>
To: "U.S. Metric Association" <[email protected]>
Sent: Sunday, 2005-10-16 04:09
Subject: [USMA:34901] Approximations (was fractions)
Using decimal form as an alternative to fractions for the final result of
a calculation is fine. You can, as has been observed below, choose any
number of decimal places to obtain the accuracy you require.
However! How do you choose the required number of decimal places? How do
you assess whether you need 1, 2, 3, .. decimal places before the result
is fit for purpose?
For example, what percentage accuracy do you achieve when you write 2/3 as
0.67?
Remember - no fractional arithmetic!
Phil Hall
----- Original Message -----
From: "Daniel" <[EMAIL PROTECTED]>
To: "U.S. Metric Association" <[email protected]>
Sent: Sunday, October 16, 2005 4:32 AM
Subject: [USMA:34897] Re: fractions
Dividing 2/3 by 1/4 is accomplished by inverting the 1/4 and multiplying.
The result is 8/3 or 2.67.
Basic concepts of fractions can and should be taught at the lower levels,
but as a form of division. 2/3 should be taught as meaning 2 divided by
3 and then show that the result is 0.667. This would be the best time to
teach significant digits when the division does not result in an integer.
In a decimal age, students need to be taught the meanings of decimals and
how to deal with them.
Fractional manipulation, such as adding, subtracting, multiplying and
dividing, should be taught as part of algebra, either ion the
introductory stage or a part of a pre-algebra course. Once the final
value is obtained, such as a number like 8/3, the answer is not complete
until the final division takes place and the result 2.67 is achieved.
There are too many American engineers who have no clue as to the concept
of significant digits in the final answer, nor when or how to round final
results. This can be traced to improper mathematical teaching in the
early years. Time wasted teaching concepts that either are over the
heads of the students or the students forget due to lack of real usage.
Yet, concepts needed to be known are not taught and poor number skills
are found among even engineers in their trades. I've lost count of how
many engineers have told me numbers like 0.4375 are valid expressions of
7/16 because that was what the calculator said. These guys had no clue
of the significance of any of the figures. In most cases a 2 digit
representation was more then enough.
But like someone posted earlier, we do this to perpetuate the bad
practices associated with inch use. Inches makes the people who use them
dumber, and it is noticeable.
Dan
----- Original Message -----
From: "m.f.moon" <[EMAIL PROTECTED]>
To: "U.S. Metric Association" <[email protected]>
Sent: Saturday, 2005-10-15 14:48
Subject: [USMA:34886] Re: fractions
Maybe this is a bit late as I have been out of town. In a recent article
on
teaching mathematics in the Los Angeles Unified School district, the
mentioned
that most teachers are teaching fraction division by the substraction
method.
Try dividing 2/3 by 1/4 -- maybe 3/4 by 1/4. There are basic classic
arithmetic algorithms that need to be learned as these can be useful in
many
other contexts which I think you will recognize if you spend a few
seconds.
BTW, on 1/3 of the math teachers have a certificate in math teaching in
that
district.
marion moon
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