Runway ID

Ah, because the REAL rounding rule, designed so that averages will not
become distorted high from rounding 1/2 up, is to round 1/2 to the
EVEN number.

I know of almost no teacher nor textbook that remembers this, much
less why it is so.

That's because it's not so.

The standard rounding rule is 5 goes up.

The catch is that you ONLY round from the digit after the one you're
rounding to. For example, .2447 rounds to .245 or to .24 or to .2
although a common error is to round (to the hundredths) as .25, because
the "rounded to the thousanths" version would end in a five. When
rounding, always round from the source, not an already adulterated version.

Jose
--
Money: what you need when you run out of brains.
for Email, make the obvious change in the address.

"Jose" wrote in message
. ..
Ah, because the REAL rounding rule, designed so that averages will not
become distorted high from rounding 1/2 up, is to round 1/2 to the
EVEN number.

I know of almost no teacher nor textbook that remembers this, much
less why it is so.

That's because it's not so.

The standard rounding rule is 5 goes up.

If you have 0.245, it is 0.24 rounded to hundreths. How is that '5 goes up?'

The rounding rules I am talking about are for preventing rounding bias in
data. If you took a big pile of numbers, rounded them all up, added them,
you would have a value that was way off of the true value of the sum.

0.247 0.25 0.2550.26 is that what you mean? That's exactly what I
stated.

The catch is that you ONLY round from the digit after the one you're
rounding to. For example, .2447 rounds to .245 or to .24 or to .2
although a common error is to round (to the hundredths) as .25, because
the "rounded to the thousanths" version would end in a five. When
rounding, always round from the source, not an already adulterated
version.

Jose

Yes, you don't round a number, then round it again.


"GeorgeB" wrote in message
...

If these runways were at the same field, your method would have runway
designators that differ by twenty degrees for runways that have a difference
in azimuth of only ten degrees. I think I'd round both in the direction
that local magnetic variation was moving.

Yes, that would be logical.

If you have 0.245, it is 0.24 rounded to hundreths. How is that '5 goes up?'

If you actually have 0.245, it is 0.25 rounded to hundredths. However,
if you actually have 0.2445, you do NOT have .0245 but a hair less than
that. In that case, you don't =have= a five to "go up".

If you took a big pile of numbers, rounded them all up, added them,
you would have a value that was way off of the true value of the sum.

True. But you don't round them all =up=. You round them all (to the
nearest). Only the ones that are ...5 and up get rounded up. The
others get truncated. Including ...0 which gets its zero truncated
(leaving the number unchanged).

0.247 - 0.25 0.255 - 0.26 is that what you mean? That's exactly what I
stated.

This is correct rounding, but it is it what George stated. He stated
"round 1/2 to the EVEN number.", which would imply .245 - .26 which is
not true. What =is= true is
..245 - .25
..255 - .26
..265 - .27

This is not "rounding 1/2 to the even number".

Jose
--
Money: what you need when you run out of brains.
for Email, make the obvious change in the address.

On Mon, 17 Oct 2005 03:18:03 GMT, Jose
wrote:

This is correct rounding, but it is it what George stated. He stated
"round 1/2 to the EVEN number.", which would imply .245 - .26 which is
not true. What =is= true is
.245 - .25
.255 - .26
.265 - .27

This is not "rounding 1/2 to the even number".

Jose, you are with the majority, and you are with what it being taught
in today's schools until higher level mathematics.

The round (exactly) half to the even is correct.

0.2449 - 0.245 - 0.24 - 0.2 but the 0.24 is not for this rule,
rather because the full precision number was under 0.5

0.3499 - 0.350 - 0.35 - 0.3 but again, rule isn't applicable
0.3501 - 0.350 - 0.35 - 0.4 but rule isn't applicable

you have to round from the full precision to the final value in 1
step; the sequential above is interesting, but not as it is done for
the reasons obvious above.

0.5 (exactly) - 0.
1.5 (exactly) - 2.
2.5 (exactly) - 2.
3.5 (again, exactly) - 4

or, fwiw, 1234.5 - 1234. and 1235.5 - 1236.

It used to be taught that way in elementary school, but was changed
between when I went to school (1950s) and when my children went to
school (1990s).

My son has a math degree, and remarked about how higher level high
school and college profs complained about having to correct the
elementaty and middle teachers teaching, but that they taught what
they were given, so it wasn't their fault.

0.5 (exactly) - 0.
1.5 (exactly) - 2.
2.5 (exactly) - 2.
3.5 (again, exactly) - 4

No.

0.5 (exactly) - 1.
1.5 (exactly) - 2.
2.5 (exactly) - 3.
3.5 (again, exactly) - 4.

Do you have a printed reference for what you espouse above?

Jose
--
Money: what you need when you run out of brains.
for Email, make the obvious change in the address.

"GeorgeB" wrote in message
...
Jose, you are with the majority, and you are with what it being taught
in today's schools until higher level mathematics.

The round (exactly) half to the even is correct.

George, you're right that rounding is often performed as you say (i.e.,
exactly half rounds to the nearest even integer), for the reason you say (to
avoid statistical biasing). But I'd quibble about calling that "the" correct
way. The function round(x) can be defined in various standard ways, and
different ways can be more useful for different purposes, but there's no
sense in which one conventional definition is the unique correct one.

http://mathworld.wolfram.com/Nearest...rFunction.html

--Gary

On Mon, 17 Oct 2005 11:03:57 -0400, "Gary Drescher"
wrote:

"GeorgeB" wrote in message
.. .
Jose, you are with the majority, and you are with what it being taught
in today's schools until higher level mathematics.

The round (exactly) half to the even is correct.

George, you're right that rounding is often performed as you say (i.e.,
exactly half rounds to the nearest even integer), for the reason you say (to
avoid statistical biasing). But I'd quibble about calling that "the" correct
way. The function round(x) can be defined in various standard ways, and
different ways can be more useful for different purposes, but there's no
sense in which one conventional definition is the unique correct one.

http://mathworld.wolfram.com/Nearest...rFunction.html

That, and Mathematica, were what I was going to reference; however,
you are correct that I had my head up that smelly place to consider it
to be "the" correct way. I've it even further up that smelly place to
get off on this when the question was on naming runways based on their
magnetic heading ... which is not a constant thing in the short or
long term, so what to do with a 5 is absolutely not going to be based
on EXACTLY anything.

Thanks for saying it so well.

George

"Jose" wrote in message
...
If you have 0.245, it is 0.24 rounded to hundreths. How is that '5 goes
up?'

If you actually have 0.245, it is 0.25 rounded to hundredths. However,
if you actually have 0.2445, you do NOT have .0245 but a hair less than
that. In that case, you don't =have= a five to "go up".

If you took a big pile of numbers, rounded them all up, added them,
you would have a value that was way off of the true value of the sum.

True. But you don't round them all =up=. You round them all (to the
nearest). Only the ones that are ...5 and up get rounded up. The
others get truncated. Including ...0 which gets its zero truncated
(leaving the number unchanged).

0.247 - 0.25 0.255 - 0.26 is that what you mean? That's exactly
what I
stated.

This is correct rounding, but it is it what George stated. He stated
"round 1/2 to the EVEN number.", which would imply .245 - .26 which is
not true. What =is= true is
.245 - .25
.255 - .26
.265 - .27

You don't round them all up? That is exactly what you are doing in your
example above.

If the digit before the last is even, and the last is five, you round DOWN
(0.245 - 0.24) If the digit before the last is odd and the last is five,
you round up. (0.255 - 0.26).

Bear with me and look at these two examples. The one on the left is a
summation of the example you have above. The one on the right is 'my' way. I
am just summing the original values and the rounded values at the bottom.

.245 - .25 .245 - .24
.255 - .26 .255 - .26
+ .265 - .27 + .265 - .26
------------ ------------
.765 - .78 .765 - .76

You can see where this will get you very quickly if you use the way you
propose.

Of course our original discussion started off regarding rounding a single
number and doing nothing with it, this is just a point of interest.



This is not "rounding 1/2 to the even number".

Jose
--
Money: what you need when you run out of brains.
for Email, make the obvious change in the address.