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# RE: FW: Precision in engineering calculations

• To: <seaint(--nospam--at)seaint.org>
• Subject: RE: FW: Precision in engineering calculations
• Date: Wed, 25 Jan 2006 12:11:50 -0800

Slow down there... you're mixing apples and oranges here.

Accounting figures and engineering figures are two entirely different types of numbers.

Even in a multimillion dollar large corporation, it would be 'material' if an employee were to pocket a couple of \$100 on a Friday afternoon from the till so he could rush off to Vegas and try to make a killing at the slots. Monday morning, security may be walking him right out of that corporation's side door and into a police cruiser for booking. The customer who wants the \$0.99 hamburger most likely will not pay \$1.00 even though its only 1% over.

Accounting figures vary in precision depending on the purpose. A year-end stockholder statement may be rounded to the nearest one-tenth of a million dollars, and the tax statement may be on the rounded whole dollar, but the individual employee gets a W-2 listing it accurate to the penny. The underlying assumption is that transactions carried out between individuals in our system of finances is based on an accuracy of one-hundredth of a dollar. Hence, the precision is flexible depending on use, but it must be accurate. Precision leads accuracy in accounting.

Engineering figures must be accurate as well, but the underlying assumption is that the degree of precision of any measurement is perhaps only 4 significant digits (within 0.1% of being 'true'). Hence the precision is fixed, or limited to the ability to physically measure something. Typically, materials in construction exhibit 5% to 10% variance from spec, so the number of significant digits at 3 is adequate. What does matter is the magnitude of those 3 digits: Is it 3.06 x 10^3 or 3.06 x 10^6? Is it 3,060 or 3,060,000? The correct order of magnitude leads to accuracy. Accuracy leads precision in engineering.

I know you probably all knew this, but it felt good to write it down again. I recently went through a similar train of thought explaining scientific notation to my 8th grader. And he doesn't round off to the nearest whole dollar on his allowance.

Best regards,

Thomas Honles, SE, PE
Los Angeles, CA

-----Original Message-----
From: Jordan Truesdell, PE [mailto:seaint1(--nospam--at)truesdellengineering.com]
Sent: Wednesday, January 25, 2006 11:18 AM
To: seaint(--nospam--at)seaint.org
Subject: Re: FW: Precision in engineering calculations

I routinely drop two digits of precision every year on my taxes, and the
IRS is fine with it.  I only use whole dollars, and the IRS suggests
doing so.

In fact, I've been known to simply ignore \$50 in my accounting. My wife,
who is controller of a medium sized corporation, has even done that with
much larger figures, and has had audits which have upheld her
"rounding".   In the financial world, it's known as whether or not the
amount is material.  For a small firm like mine, everything over \$100 is
material. For a large corporation, several thousand dollars may not be
material (though it often is).

To believe that you have as much accuracy as you have precision will
(that's 0.00001") won't do you any good if it's not zeroed, and your
measurement won't be very repeatable if you're holding the gauge block
in your hand while you take the measurement.

I would tend to side with Tim's professors in this one.  Now, if someone
could talk to my fundamentals of engineering professor about the 5
points I lost for placing the middle horizontal line of  a capital "E"
slightly below the center of the vertical line, rather than slightly
above, I'm right there with you!

Jordan

Ray Pixley wrote:

> Those teachers were (1) wrong to do that, (2) short sighted, (3)
> unprofessional, and (4) think a slide rule is a high tech bell and
> whistle device. But that's life when they have that much power over you.
>
> Anyway, significant figures are an issue if you are looking for a
> number that is the difference between two numbers that are nearly the
> same.  When subtraction is being used, it matters.  (Maybe other
> operations also.)   If you don't have enough significant figures, you
> get garbage.  No amount of tap dancing justification will be able to
> overcome that deficiency.
>
> Now, ask those so called "teachers" if they round their taxes up to
> the next thousand dollars, simply because it is "approximately" what
> is due.  Ask if when they see a penny on the street, do they pick it
> up or consider it worthless?  If not a penny then what about a dime?
> A quarter?
>
>
>
> ----Original Message Follows----
> From: "Timothy Allison" <t_allison(--nospam--at)illinoisalumni.org>
> To: <seaint(--nospam--at)seaint.org>
> Subject: Re: FW: Precision in engineering calculations
> Date: Wed, 25 Jan 2006 09:08:16 -0800
>
> We were taught significant figures (and how to use them) in school.  A
> couple teachers would go so far as to deduct a point or two for using
> too many sig figs.  In practice, I ignore the rules and take it out to a
> "clean" number - your example of 12319.82 vs. 12300 would be 12320 to
> me.
>
> I do agree with your thought that calculators give a false sense of
> accuracy.  If you take something simple like "25000 - 12000", you're
> still entering five digits regardless of there possibly being as few as
> two significant figures, so writing the result with five significant
> figures is kind of a natural reaction.
>
>
> -----Original Message-----
> From: Sherman, William [mailto:ShermanWC(--nospam--at)cdm.com]
> Sent: Wednesday, January 25, 2006 10:53 AM
> To: seaint(--nospam--at)seaint.org
> Subject: Precision in engineering calculations
>
> Do engineering schools still teach the concept of "significant digits"
> in design calculations? I generally like to show results to 3
> significant digits (e.g., 12,300 lbs vs 12,319.82 lbs); although I
> consider the real accuracy probably closer to 2 digits for most design
> work. But I find that young engineers often show results such as 123.47
> ft-kips. There are occasions when more significant digits are
> warranted, such as when subtracting two large numbers, e.g. 12,319 lbs
> minus 11,898 lbs. But most of the time such accuracy in numbers is not
> warranted. For manual calculations, I feel that it takes extra time to
> enter and write those extra digits, and it implies a greater accuracy
> than is reality.
>
> When I started college in 1970, I used that ancient device called a
> slide rule. By the time I graduated, I could afford one of those
> new-fangled calculators. I think that having to use a slide-rule gave
> me a better understanding of significant digits, whereas calculators and
> computers give people a false sense of design accuracy.
>
> Nevertheless, I once did some design work for nuclear power projects and
> was told that if my results showed a calculated stress of 24.1 ksi vs an
> allowable stress of 24 ksi, the member size would need to be increased.
> But that was less about accuracy and more about fear that someone would
>
>
> William C. Sherman, PE
> (Bill Sherman)
> CDM, Denver, CO
> Phone: 303-298-1311
> Fax: 303-293-8236
> email: shermanwc(--nospam--at)cdm.com
>
> Scott Maxwell wrote:
>
> "And I agree with you on the whole knat's rear arguement...it is not
> needed or even warranted frequently in the "structural world". And it
> is many times not even useful in repeative situations...in steel design,
> one usually saves more money by having the same beam over and over and
> over again rather than getting the absolute lightest members possible.
> Not to mention that the concrete actually used likely is not going to
> have the exact f'c that you used in design nor the steel to have the
> exact fy that you used. So, doing precise calculations to some 5th
> decimal place (although it does somewhat depend on the units used) is
> typically a waste of time. I learned that one back in school when my
> concrete professor "yelled" at me for using two or more decimal places
> in my homeworks and pointed out that if my capacity was within roughly
> 5% or less of demand, I was likely "good to go"."
>
>
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