Sent: Sunday, August 08, 2004 4:29 PM
To: CF-Talk
Subject: Re: Val function seems buggy
Now it goes to the definition of number, 0, as 1 or 2, is A NUMBER.
021 IS DIFFERNT FROM 21.
No, it isn't - at least not mathematically. In math you use significant
digits only - meaning, basically, only those digits that would affect the
outcome in an operation. Since "20 + 1 = 21" and "020 + 1 = 21" the leading
zero in the section operation is "insignificant" - it doesn't matter to the
math. So it's not considered part of the number.
This is a really simple explanation and a really bad explanation of
"significant digit" which means something different in science. In more
precise terms significant digits are only those that contain value, not
those used just as place holders. In this way the number 60000, for
example, has only one significant digit - the digit "6" - the three zeros,
while important, don't contain any value and are just used to force the only
significant digit into the proper place.
Another, perhaps easier, way to consider this is the way numbers are written
in scientific notation. When you write "60000" you've got a number, but
information is missing as to purpose of the zeros - are they just there to
push the 6 into place or were they measured? In this case you have to
assume that they're insignificant.
But if we write 6*10^4 then that shows us that 6 is the only significant
digit. But you can also write 6.000*10^4 then that indicates that three of
the zeros are indeed significant (usually that they were specifically
measured) - however it also means that one is not. This happens a lot with
measurements.
Let's say I have a radar gun that could measure speed in 10 mph increments.
When I clock a car doing "50mph" I know that the speed is at least 50mph but
not more than 60mph. So the number "50" in this case has only significant
digit: the 5 (since the zero is needed to "push" the 5 over, but was not
measured itself). So in scientific notation you'd write "5*10^1" (well, I
think - my scientific notation is rusty).
But now a friend comes along and his radar gun measures in 1mph increments -
when he clock's a car doing "50mph" he knows that the speed is at least
50mph bot not more than 51mph. In this case the number "50" has two
significant digits (since both digits were measured). You'd write
"5.0*10^1" is scientific notation to indicate that the zero is indeed needed
and significant.
Now one of the most fundamental rules of determining significance (so
fundamental that it's often not even mentioned) is that any zeros to the
left of the last significant digit or decimal point are insignificant. They
are doubly damned since they 1) don't change the value of the number and 2)
can't EVER be measured (how would you specifically measure the zero in
"021"?)
CF is doing the right thing here since val() is a numeric function.
Jim Davis
[Todays Threads] [This Message] [Subscription] [Fast Unsubscribe] [User Settings] [Donations and Support]
