Serious SI Question

[zdas04]

What is the convention for exponating units with multiple letters? I saw "100 km³" the other day and can't for the life of me figure out if the intent was "100 thousand cubic meters (10⁸L)" or "100 cubic kilometers (10¹⁴L)".

MathCAD says that 100 km³=100 (km)³" but MathCAD treats "km" as a single unit. Is that the official convention or just a MathCAD convention?

In my terms, 100 cubic kilometers is 3.5 TCF and 100,000 cubic meters is 3.5 MMCF.

David

 

[TGS4]

David - my understanding has always been that when multiple letters are used for the abbreviation of a unit, and an exponent is used, the exponent applies to the entire unit.

For example:
1 mm³ = 1 cubic millimeter = 0.001 mL - not 1/1000 of a cubic meter
1000 cm³ = 1L = one thousand cubic centimeters - not 1000/100 cubic meters.

In this case, the MathCAD interpretation is what my understanding of correct was.

 

[ivymike]

while I agree that the mathcad version seems correct, the cited example of km^3 seems an improbably large unit of volume.

 

[cswilson]

I've been seeing km^3 figures bandied about a lot lately, particularly in reporting on earth sciences. You'll see a breathless report that Greenland's glaciers are disappearing at a rate of 100 km^3 per year, or some such, which as you say, seems improbably large. But when you compare it to the millions of km^3 total, it is a drop in the bucket, and probably within the range of measurement error...

 

[Skogsgurra]

To expand on TGS4's comment. Yes, I agree that the exponent applies to the km as a unit. That is understood, as is the use of cm3 for a milliliter.

It gets trickier when other prefixes are being used. Like Tm3 for teracubicmeter or fm2 for femtosquaremeter - not so sure there is any valid standard in such cases. But my first guess is that the exponent applies to the unit and not to the meter alone.

Gunnar Englund

http://www.gke.org

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Half full - Half empty? I don't mind. It's what in it that counts.

 

[VEBill]

To quote a very wise man, " ...the exponent applies to the unit."

In this case, one hundred cubic-kilometers.

If it was "1M km³", then that would mean one million cubic-kilometers, for example a cube 100km on each side.

One hundred kilometers cubed should be written: "(100km)³".

The problem with most news outlets is that they will totally mess up any numerical values and units. They can't be trusted with anything numerical. Come to think of it, they're not very good with anything factual for that matter...

 

[btrueblood]

Zdas,

Here is your definitive, serious answer.

NIST Special Publication 811, 1995 Edition, "Guide for the Use of the International System of Units (SI)"

states:

6.2.3 Inseparability of prefix and unit

The grouping formed by a prefix symbol attached to a unit symbol constitutes a new inseparable symbol (forming a multiple or sub-multiple of the unit concerned) which can be raised to a positive or negative power and which can be combined with other unit symbols to form compound unit symbols.

Examples : 2.3 cm³ = 2.3 (cm)³ = 2.3 (10^-2 m)³ = 2.3 3 1026 m³
...

Prefixes are also inseparable from the unit names to which they are attached. Thus, for example, millimeter, micropascal, and meganewton are single words.

A pdf copy is attached below.

http://files.engineering.com/getfil...e8f-4832-ac9f-91f4e6e88148&file=NISTsp811.pdf

 

[btrueblood]

woops. forgot to re-parse the last part of the example string so it would post here correctly. Correcting the last equivalent gives:

Examples : ... = 2.3 x 10^-6 m³

 

[zdas04]

Thank you all.

btrueblood,
Thank you for finding that. I find it hilarous that an official SI publication posts a very clear example using a non-SI unit (cm).

David

 

[ScottyUK]

It's an American dcument by the same outfit who makes your gallons smaller than ours. You can't blame S.I. for that David!


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If we learn from our mistakes I'm getting a great education!

 

[Skogsgurra]

They also manipulated the horsepower..

Gunnar Englund

http://www.gke.org

--------------------------------------
Half full - Half empty? I don't mind. It's what in it that counts.

 

[zdas04]

Sorry, I thought it was from ISO, now I see it was from NIST. They're a pretty impressive bunch, but they do have a very firm opinion of their own "rightness".

David

 

[VEBill]

...the same outfit who makes your gallons smaller than ours...

Suspicion leads me to Wiki:

Wiki: "A wine gallon is a unit of capacity that was used routinely in England as far back as the 14th century, and by statute under Queen Anne since 1707. Britain abandoned the wine gallon in 1826 when it adopted imperial units for measurement. The 1707 wine gallon is the basis of the United States' gallon, as well as other measures."

So, contrary to popular assumption, it's those tradition-hating, chasing-the-latest-19th-century-fad, Brits that adopted that new-fangled (!) "Imperial" gallon in 1826. ;-)!!

 

[ScottyUK]

How typical of our upstart colony to refuse to do as the Empire commanded.


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If we learn from our mistakes I'm getting a great education!

 

[IRstuff]

The NIST document is essentially a translation of the official SI brochure from BIPM: Le Système international d’unités:

http://www.bipm.org/utils/common/pdf/si_brochure_8.pdf

Do a search on "inseparable" and you'll see the French version on the first hit, and the English translation on the second hit.

TTFN

FAQ731-376
Chinese prisoner wins Nobel Peace Prize

 

[Skogsgurra]

Nice to have that document available, thanks to IR.

You probably heard it before, but deserves an encore: "US is going metric, inch by inch"

Gunnar Englund

http://www.gke.org

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Half full - Half empty? I don't mind. It's what in it that counts.

 

[btrueblood]

Err, David, not to be too pendantic. Well, yes, to be pedantic. The prefixed SI units cm, mm etc. are all valid SI units (see 4.4), just not base SI units. Derived constants from non-base units (e.g. dynes and other manifestations of CGS) are supposed to be avoided (section 5).

 

[BigInch]

It was bound to be a futile effort. England never got rid of the USGal because they ran out of oak. The oak casks used to age burbon whiskey were made in Tennessee, the empties recycled to Spain for curing brandy and sherries with oak and a little added burbon flavor which was highly regarded back up in UK.

http://www.lochlomonddistillery.com/cooperage.htm

We are more connected to everyone in the world than we've ever been before, except to the person sitting next to us. Lisa Gansky

 

[TheTick]

My old boss used to say there are only three countries left that are not metric, and one of them is Libya. Curious about the other one. Any ideas?

 

[hokie66]

I'm with David on cm. Centimetre is not an SI unit, no matter what they say. Not for engineers, anyway. Dressmakers, maybe.