Has Scientific Notation Changed???

SkyHog

SkyHog

Touchdown! Greaser!
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Everything Offends Me
So Brianna is in a Biology class, and she's showing me her homework, and the teacher specifically stated that the scientific notation must be:

n.nn x 10^x

That is to say....

.002 MUST BE written as:

2.00 x 10 ^-3

I seem to remember it being perfectly acceptable to use
2x10^-3

When did it become standard to over complicate scientific notation?

Also - the teacher requires rounding in instances where there are more decimal places....for example:

.1111125 becomes
1.11x10^-1

I seem to recall the correct answer being
1.111125x10^-1

It seems small, but I'm pretty sure my fiancee's teacher is retarded....am I wrong?
 
The extra (or removed) digits are changed due to significant figures!

2.00 x10^-3 is a different number from 2x10^-3.

Basically, the first represents the numeric set from 1.995 to 2.005, whereas the second is 1.5 to 2.5!

In the last case, she most likely doesn't have the applicable significant figures to represent that decimal.
 
SkyHog said:
So Brianna is in a Biology class, and she's showing me her homework, and the teacher specifically stated that the scientific notation must be:

n.nn x 10^x

That is to say....

.002 MUST BE written as:

2.00 x 10 ^-3

I seem to remember it being perfectly acceptable to use
2x10^-3

When did it become standard to over complicate scientific notation?

Also - the teacher requires rounding in instances where there are more decimal places....for example:

.1111125 becomes
1.11x10^-1

I seem to recall the correct answer being
1.111125x10^-1

It seems small, but I'm pretty sure my fiancee's teacher is retarded....am I wrong?
Click to expand...

The number of significant digits should match the accuracy of the original measurements.

So, if I tell you something is 1 foot long, 1/3 of it would be .3 feet (or 3*10^-1). If I told you that it was 1.0000 feet long (implying that I had a MUCH better measure of the length - I measured to about a thousandth of an inch ) then 1/3 would be about .333333 (3.3333*10^-1) feet...

So, if the teacher is saying that you always use three significant digits, no matter what, the teacher is sadly misinformed.

For ".1111125" the answer depends on how many of those digits are significant.
 
You're right on the first, wrong on the second.

The main point of scientific notation is one to easily right very large or small numbers, and second to indicate significant digits.

Say you have the number 2000.

With 1 significant digit you can write it 2000 or 2*10^3

With 2 significant digits it is written 2.0*10^3.

With 3 sig digits it is written 2.00 * 10^3.

So, it seems that you're fiancees teacher requires 3 significant digits in all cases.

".1111125 becomes
1.11x10^-1"

is correct for 3 significant digits.
 
SkyHog said:
So Brianna is in a Biology class, and she's showing me her homework, and the teacher specifically stated that the scientific notation must be:

n.nn x 10^x

That is to say....

.002 MUST BE written as:

2.00 x 10 ^-3

I seem to remember it being perfectly acceptable to use
2x10^-3
Click to expand...

You are correct 2.00 x 10 ^ -3 indicates a level of precision that was not in the original notation. Converting the back would result in .00200.

SkyHog said:
When did it become standard to over complicate scientific notation?

Also - the teacher requires rounding in instances where there are more decimal places....for example:

.1111125 becomes
1.11x10^-1

I seem to recall the correct answer being
1.111125x10^-1

It seems small, but I'm pretty sure my fiancee's teacher is retarded....am I wrong?
Click to expand...

By itself you are correct here as well, But when used with other numbers could initiate a discussion in significant digits.

Brian
 
Capt. Geoffrey Thorpe said:
The number of significant digits should match the accuracy of the original measurements.

snip...

So, if the teacher is saying that you always use three significant digits, no matter what, the teacher is sadly misinformed.

.... snip
Click to expand...

Agreed!

If the original information was .002, then transforming it to 2.00 x 10^-3 is in error by adding two additional significant figures of information that was not present in the original.

That teacher needs some remedial training...
 
ah, its an exponential.
test
232

so apparently you cant do a superscript on forums?
 
sup and sub tags are enabled

C6H2(NO2)3CH3

9.3x107

Just take out the spaces in:
C[ sub ]6[ /sub ]H[ sub ]2[ /sub ](NO[ sub ]2[ /sub ])[ sub ]3[ /sub ]CH[ sub ]3[ /sub ]
9.3x10[ sup ]7[ /sup ]
 
Let'sgoflying! said:
It sure has changed, what the heck does the hat thing mean??
Click to expand...

Let'sgoflying! said:
ah, its an exponential.
test
232

so apparently you cant do a superscript on forums?
Click to expand...

Yep...the hat thing indicates an exponential. I've seen a few different ways of expressing these on forums...based on various computer languages, calculators, and spreadsheets.

6.023*10^23 = 6.023*10**23 = 6.023E23
 
SkyHog said:
When did it become standard to over complicate scientific notation?
Click to expand...

The teacher is wrong here. 0.002 should be written 2 x 10^-3. If it was written 2.00 x 10^-3, that would incorrectly imply the precision of the measurement was 0.00200, i.e., to 5 places.

SkyHog said:
Also - the teacher requires rounding in instances where there are more decimal places....for example:

.1111125 becomes
1.11x10^-1

I seem to recall the correct answer being
1.111125x10^-1
Click to expand...

That depends on the precision of the measurement. If the number .1111125 was arrived at by, say, a division of two numbers with no more than 3 significant digits each, then this number should be expressed as 0.111, or 1.11 x 10^-1. All those extra digits are physically meaningless since they are beyond the precision of the measurements which produced this number.
 
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jstro said:
The teacher is wrong here. 0.002 should be written 2 x 10^-3. If it was written 2.00 x 10^-3, that would incorrectly imply the precision of the measurement was 0.00200, i.e., to 5 places.



That depends on the precision of the measurement. If the number .1111125 was arrived at by, say, a division of two numbers with no more than 3 significant digits each, then this number should be expressed as 0.111, or 1.11 x 10^-1. All those extra digits are physically meaningless since they are beyond the precision of the measurements which produced this number.
Click to expand...

Sig figs! Reminds me of freshman engineering days.

And a lot of people don't understand the difference between precision and accuracy, too.


Trapper John
 
My guess is that the Instructor (faculty, TA, casual?) is taking this opportunity to teach his or her Padwan learner as much about scientific notation as he or she can. Odds are this Biology course is the only science course that the young lady will have, thus they put as much "science" in it as they can manage.
 
Sheesh -- and you guys complain about legal mumbo-jumbo?


:D:D
 
Try reading a scientific paper in a peer-reviewed journal. You'll never complain about legaleze again.
 
steingar said:
Try reading a scientific paper in a peer-reviewed journal. You'll never complain about legaleze again.
Click to expand...

Unless you read a paper in a Law Review about some obscure legal topic...then you'll be back to complaining about legaleze!
 
jstro said:
The teacher is wrong here. 0.002 should be written 2 x 10^-3. If it was written 2.00 x 10^-3, that would incorrectly imply the precision of the measurement was 0.00200, i.e., to 5 places.
Click to expand...
Uh, no.

If it "worked that way", then 2.00 x 10^-4 would be 6 significant figures, and 2.00x10^-14 would be 16 significant figures, neither of which is correct.
-harry
 
mantakos said:
Uh, no.

If it "worked that way", then 2.00 x 10^-4 would be 6 significant figures, and 2.00x10^-14 would be 16 significant figures, neither of which is correct.
-harry
Click to expand...

It does work that way. Two-one-thousandths is assumed to have one significant figure unless it is followed by another digit. The preceding zeros are considered placeholders.
 
Clark1961 said:
It does work that way. Two-one-thousandths is assumed to have one significant figure unless it is followed by another digit. The preceding zeros are considered placeholders.
Click to expand...
I think we may all be saying the same thing, but I may have misunderstood what an earlier poster was saying.

When he said: "If it was written 2.00 x 10^-3, that would incorrectly imply the precision of the measurement was 0.00200, i.e., to 5 places", I thought he was implying that 2.00x10^-3 had 5 significant figures.
-harry
 
mantakos said:
I think we may all be saying the same thing, but I may have misunderstood what an earlier poster was saying.

When he said: "If it was written 2.00 x 10^-3, that would incorrectly imply the precision of the measurement was 0.00200, i.e., to 5 places", I thought he was implying that 2.00x10^-3 had 5 significant figures.
-harry
Click to expand...


I agree with you that the poster claiming 5 sig figs was sending a mixed message. They got the first half of their statement right and then screwed it up on the home stretch.

And, to my embarrassment, I failed to note the claim of 5 sig figs. I just looked at the first half of the post and saw that it was correct. My apologies.
 
Clark1961 said:
I agree with you that the poster claiming 5 sig figs was sending a mixed message. They got the first half of their statement right and then screwed it up on the home stretch.

And, to my embarrassment, I failed to note the claim of 5 sig figs. I just looked at the first half of the post and saw that it was correct. My apologies.
Click to expand...

Yes, thanks for catching that error. 2.00 x 10^-x, no matter what "x" is, is indeed 3 significant digits.
 
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mantakos said:
Uh, no.

If it "worked that way", then 2.00 x 10^-4 would be 6 significant figures, and 2.00x10^-14 would be 16 significant figures, neither of which is correct.
-harry
Click to expand...

Thanks for catching that, I phrased that badly. It is indeed 5 places, but only 3 of those remain significant.
 
jstro said:
No, I was completely correct all the way through. I'm not sure how someone might have misconstrued me saying that 0.002 had 5 significant figures, especially since in that same sentence I did say that such an assumption would be incorrect. Significant digits is simple stuff, folks. In any case, sorry if I said something that was unclear.
Click to expand...

No, you weren't completely correct all the way through. In particular, 2.00 * 10^-3 only has three significant digits. That is all that should be said. When you say that somehow it incorrectly implies five significant digits you demonstrate a gross misunderstanding of placeholders vs accuracy digits.

I spent way too many semesters as a graduate teaching assistant. In short, don't give a bad example and then claim clarity. It just doesn't work.
 
Clark1961 said:
No, you weren't completely correct all the way through. In particular, 2.00 * 10^-3 only has three significant digits. That is all that should be said. When you say that somehow it incorrectly implies five significant digits you demonstrate a gross misunderstanding of placeholders vs accuracy digits.

I spent way too many semesters as a graduate teaching assistant. In short, don't give a bad example and then claim clarity. It just doesn't work.
Click to expand...

I phrased something badly, and when I realized where, I edited my response accordingly. I said that 2.00 x 10^3 was another way of writing 0.00200 which was 5 places, but what I should have emphasized that only 3 of these remain significant, which didn't come through as I had intended.

I appreciate your experience as a graduate assistant. Myself I am a PhD engineer of 12 years. Even so, I still mis-communicate sometimes.
 
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I'm glad to see that many here seem to understand this. Many times, I had thought I was the only one who did when the engineers at a large company specified something such as "shall be less than or equal to 2.0V" and then call it out of spec when the actual meter measurement is 2.003.
 
skidoo said:
I'm glad to see that many here seem to understand this. Many times, I had thought I was the only one who did when the engineers at a large company specified something such as "shall be less than or equal to 2.0V" and then call it out of spec when the actual meter measurement is 2.003.
Click to expand...
I ran into that a few times in torque specifications at my former place of employment. "100, +0/-8 ft.lbf torque. Set torque wrench to 100ft.lbf."

Doing so, means taking a torque wrench, whose accuracy at the 100ft.lbf cardinal point is +/-4ft.lbf, and using it to torque said bolt. Well, doing so, the mechanic could be torquing the fastener to as much as 104ft.lbf, which could cause the reactor to explode and all the Guernsey cows downwind to give off buttermilk:rolleyes:. Of course, we all "knew" the real intent; however, the NRC, being a government entity, didn't. Thus we would find ourselves performing a pre-use calibration of said particular wrench (and adjusting it for 100ft.lbf (now +/-1ft.lbf--the accuracy of the calibrator), use the wrench for that specific job, then immediately performing a post-use calibration to verify the wrench was still set to the proper value. And hoping the wrench didn't get fixed surface contamination on/in it while it was being used in the "radiologically-controlled area."
What a pain in the rump and neck, it was--all to meet not the spirit, but the letter of the law...

Kinda like FAA regs sometimes... :eek::D
 
Capt. Geoffrey Thorpe said:
The number of significant digits should match the accuracy of the original measurements.
Click to expand...
I had a high school physics teacher who beat that to death, and then well into the afterworld. 2 x 2 = 4, but 2.00 x 2.00 = 4.00, and don't you ever forget it!

And I didn't.

So, if the problem in physics class is 2.1 x 2.1, the answer is 4.4, not 4.41 (only two significant digits in the input data, so only two in the output. But if the problem is 2.10 x 2.10 (three significant digits), then the answer is 4.41 (also three significant digits), and nothing else. Of course, this is only for the sciences (physics, chem, bio, etc) and engineering -- in math class, the answer is 4.41 either way.

And if you want, we can start a thread of jokes about physicists, mathematicians, and engineers -- I have a good collection to get us going.

:sigh:
 
msupples1 said:
Say you have the number 2000.
Click to expand...
Assuming that "." at the end is a period, not a decimal point, if you have "the number 2000," all you have is an integer with no defined precision. It's good for counting things one by one (like what year this is on the calendar), but not for measuring things (like determining how old something is using carbon dating).

If you have a measurement, then with "the number 2000," you have an imprecision statement of the measurement. It could be 2X10^3 (one significant digit, which tells you only that the quantity appears closer to 2000 than to either 3000 or 1000), or 2.0x10^3 (two significant digits), or 2.00000000x10^3 (nine significant digits, i.e., 2000.00000 -- which means closer to 2000.00000 than to either 2000.00001 or 1999.99999).

IOW, the placement of the decimal point and the number of trailing zeros are important in determining the precision of the measurement, and the number of significant digits to use in the result of any succeeding computation for which that measurement is an input. That's why we use scientific notation and follow the rules discussed above when using it.

And anyone who learned on a slide rule rather than a digital calculator should fully understand this.
 
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