-1 exponent what does it do?

I'm trying to understand this chemical formula. The formula says add .01mg/L-1 with -1 being superscript. The L stands for liter or 1000ml. Does this mean to figure out how much liquid in liters,(L), that I should divide 1 by L (1/1000), to give me .001 liters?

Thank you!
Frank

\(\displaystyle mgL^{-1}\) is milligrams per Liter ... \(\displaystyle L^{-1} = \frac{1}{L}\)

\(\displaystyle mg/L^{-1} = mgL\) ... milligram-liters, which I've never heard of.

Hi Skeeter,

I think, from a response by a notable Dr., that perhaps the formula should have been writen mg/l-1 (with a lowercase L). The use of a lower case L with the superscript -1 is used by different countries when writing formulas. l-1 and L are the same thing.

Thank you Skeeter!
Frank

Just incase you are wondering, I'm mixing a forumla of plant hormones for plant tissue culture, (growing plants in test tubes). It's a hobby of mine.

What is it? From a single small leaf section or bud of a plant you can get 4 to more than 20 plants per month. From each of those plants you can get the same amount. If you do the math and only get 4 plants from each one per month, in one year you will have 1048576 plants. Take a highly valued plant, some of which can cost +100 dollars each, well you get the picture. If you are interested, you can check out how to do it at http://tech.groups.yahoo.com/group/hometissueculture

Thanks again,
Frank

mathboy said:

The use of a lower case L with the superscript -1 is used by different countries when writing formulas. l-1 and L are the same thing.

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While "l" (lower-case ell) is sometimes used to indicate the SI unit "litres", the potential for confusion with "1" (numeral one) has resulted in many using "L" (upper-case ell) instead. This appears to be accepted as proper procedure according to authoritative sources.

However, I have never heard of "1/l" being used to stand for "litres", nor could I locate any reference to this. (In fact, it would appear that international standards specifically forbid this.) I'm afraid your online reference, being a members-only forum, was not viewable.

Please reply with documentation, so that this confusion may be avoided in future discussions. Thank you for your help.

Eliz.

Hi Eliz,

The scientific journal in which has the l-1 was from a university in Spain. I'm not sure now if it was a typo in translation or that's the way Liter can be written in a formula. It seems redundant to me if Liter is written this way too. I also have seen it, rarely, in other scientific journals usually from countries other than the U.S. So, I'm thinking that it can be an accepted method for displaying a Liter. On this site they express Liter as l-1 when describing Moles per Liter http://tinyurl.com/4k66vt

Dr. Ronald de Fossard, author and scientist in plant biology, seems to know that Liter can be written this way and sent me an email telling me so. I respect his opinion. He has been around a long time and his name is recognized around the world in the scientific community.This is the email from Dr. Ronald de Fossard.

"L stands for litre.
l-1 (lower case l with superscript -1) stands for litre.

Dr. Ronald de Fossard
http://users.bigpond.net.au/rdefossard"

Thank you,
Frank

mathboy said:

On this site they express Liter as l-1 when describing Moles per Liter http://tinyurl.com/4k66vt

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Actually, no; they express "litres" as "L". Since "moles per litre" means "moles divided by litres", the units are "mol/L" or "mol L[sup:3oa49ebf]-1[/sup:3oa49ebf]", since "L[sup:3oa49ebf]-1[/sup:3oa49ebf]" means "1/L" and (mol)(1/L) = mol/L. The referenced site is using the regular notation.

mathboy said:

This is the email from Dr. Ronald de Fossard: "L stands for litre. l-1 (lower case l with superscript -1) stands for litre..."

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From everything I can find, this person has made up his own personal notation. :shock:

Eliz.

Hi Eliz,

>From everything I can find, this person has made up his own personal notation.
Hmmm... it would seem everyone is making this up.

>Actually, no; they express "litres" as "L". Since "moles per litre" means "moles divided by litres", the units are "mol/L" or "mol L-1", since "L-1" means "1/L" and (mol)(1/L) = mol/L. The referenced site is using the regular notation.

mg/L or mg/L-1 is how many milligrams per there are in a 1 Liter solution.
mol or M/L is how many mols, weight of a substance, there is in 1 Liter.

A quick look around and I was able to find a few journals that use the same expression L-1. Below are just a few of them.

Callus Induction and Organogenesis from explants of Aconitum heterophyllum
http://www.ansijournals.com/biotech/2006/287-291.pdf

Regeneration of plantlets from node-derived callus in Aegle marmelos Corr.
http://www.ansijournals.com/biotech/2007/72-75.pdf

Rapid plant regeneration from Gerbera jamesonii Bolus callus cultures
http://hrcak.srce.hr/file/5768

Micropropagation of Woody Legume (Albizia lebbeck Through Tissue Culture)
http://ansijournals.com/pjbs/2004/1099-1103.pdf

Application of in vitro Tissue Culture Techniques for Propagation of Amygdalus communis L. (Almond)
http://www.ansijournals.com/biotech/2006/49-52.pdf

Effect of Plant Growth Regulators on in vitro Propagation fo Vitis ficifolia Hybrid Grape.
http://www.ansijournals.com/ajps/2005/466-471.pdf

Efficient transformation mediated by Agrobacterium tumefaciens with a ternary plasmind in Pharbitis nil Morning Glory
http://db1.wdc-jp.com/pdf_store/jspcmb/ ... 22_295.pdf

Large Scale Plant Regeneration in vitro from Leaf Derived Calluse Cultures of Pineapple
http://www.ansijournals.com/ijb/2005/128-132.pdf

In vitro Rooting and Ex vitro Plantlet Establishment of BARI Bannana
http://www.ansijournals.com/ajps/2004/196-199.pdf

Can a general shoot proliferation and rooting medium be used for a number of carnation cultivars?
http://www.bioline.org.br/pdf?jb06004

Micropropagation of gladiolus Peach Blossom through enhanced release of auxillary buds.
http://www.jtropag.in/index.php/ojs/art ... ad/144/138

In vitro Rapid Regeneration from Cotyledon Explant of Native olive
http://www.ansijournals.com/ajps/2004/31-35.pdf

FACTORS MODIFYING REGENERATION IN VITRO OF ADVENTITIOUS SHOOTS IN FIVE RED RASPBERRY CULTIVARS
http://www.insad.pl/files/journal_pdf/j ... 1_2006.pdf

Frank

mathboy said:

Hmmm... it would seem everyone is making this up.

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How so? Everybody else agrees that, in general, "to the minus one power" means "divided by", and, in particular, L[sup:2wgcnzmm]-1[/sup:2wgcnzmm] = 1/L means "divided by the number of litres" or "per litre" (depending upon the context and the available information). Thus far, there seems to be only the one source for your notation.

mathboy said:

A quick look around and I was able to find a few journals that use the same expression L-1.

Click to expand...

Yes, the notation mgL[sup:2wgcnzmm]-1[/sup:2wgcnzmm] = mg/L (meaning "milligrammes per litre") is very common for measuring density; that's why the first tutor mentioned it. It's your notation, mg/L[sup:2wgcnzmm]-1[/sup:2wgcnzmm] = mg-L, which is odd.

It should be noted that in every instance thus far (including all of your references), the "L[sup:2wgcnzmm]-1[/sup:2wgcnzmm]" notation has meant "divided by the number of litres" or "per litre", not just plain "litres". I'm sorry, but L[sup:2wgcnzmm]-1[/sup:2wgcnzmm] = 1/L no more means "litres" than 3[sup:2wgcnzmm]-1[/sup:2wgcnzmm] = 1/3 means "three".

I regret the offense it seems I have caused by disagreeing with your friend, but I'm afraid multiplication and division are simply not the same process.

Eliz.

Hi Liz,

No, I agree with you and that was my first interpretation of the formula.
The top number in L-3, 1 should be divided by the bottom number multiplied by the superscript,(3x3), or 1/9 correct? So, shouldn't L-1 be 1/1 or just 1?

I'm familiar with these ratios of plant growth regulators and at those amounts they should be mixed with 1 liter and not a smaller amount. So, that makes me think that L-1 equals L

Frank

mathboy said:

The top number in L-3, 1 should be divided by the bottom number multiplied by the superscript,(3x3), or 1/9 correct?

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To learn how exponents work in general (it's multiplication, but not by the power), try the following:

. . . . .Google results for "exponent rules"

To learn how negative exponents work in particular, try here:

. . . . .Google results for "negative exponents"

I'm not sure where your "L[sup:uum68m80]-3[/sup:uum68m80]" is coming from...? (I'm not familiar with any meaning for the cube of a volume.) But L[sup:uum68m80]-3[/sup:uum68m80] = 1/L[sup:uum68m80]3[/sup:uum68m80], not 3L, 3x[sup:uum68m80]3[/sup:uum68m80], 1, or 1/9. You'll understand why not once you've studied a few lessons.

Eliz.

Hi Eliz,

Oooops, I ment to say L-3 should be 1 liter divided by 3*3*3 or 1/27. Correct?

In L-1, it would be 1 liter divided by 1 which equals 1 liter (1/1).

Frank

mathboy said:

...L-3 should be 1 liter divided by 3*3*3 or 1/27. Correct?

Click to expand...

No; L[sup:24wlv34h]-3[/sup:24wlv34h] does not equal 3[sup:24wlv34h]-3[/sup:24wlv34h]L. And L[sup:24wlv34h]-1[/sup:24wlv34h] does not equal L; it still equals 1/L.

Eliz.