Sig fig question: Adding 3000 + 1.234

[phinds]

However this is very different from the notion of a "significant figure quiz" where you are presented with ridiculous questions like "what is 3,000 + 1.234" and are supposed to guess or memorize arbitrary rules for inferring what is required.

Agreed

 

[bob012345]

I tutor high school students in chemistry. Sig figs is an important topic in the class so I best understand it.

If the lab notes say add 3 grams of something should one round everything to 1 significant digit?

 

[Office_Shredder]

If the lab notes say add 3 grams of something should one round everything to 1 significant digit?

Add 3 grams isn't a measurement, so doesn't take sig figs. The amount you measure and then add is a measurement. If you aren't precise enough to say it was 3.0 grams, then yeah you're stuck

 

[malawi_glenn]

My 2 cents:

3000 has one, two, three or four significant digits. It can mean anything and depends on what convention you are going to use.
Here is one such convention, see rule 6
https://ccnmtl.columbia.edu/projects/mmt/frontiers/web/chapter_5/6665.htmlThis is why we invented scientific notation, to avoid such confusion.

 

[phinds]

This is why we invented scientific notation, to avoid such confusion.

No, it is not. We invented scientific notation so as to not have to write out dozens of zeros for large numbers.

 

[malawi_glenn]

No, it is not. We invented scientific notation so as to not have to write out dozens of zeros for large numbers.

Yeah true, that is the main reason ;)

 

[TeethWhitener]

As others have pointed out, sig figs are basically just a lazy person's error analysis, and the answer will depend on the convention used (the one OP references is the one I learned in high school (late 90's): that "3000" has one sig fig while "3000." with a decimal after the trailing zero has 4 sig figs, etc.). That said, OP is a high school chemistry tutor and many high school assignments nowadays are on computers, coded poorly, with basically no tolerance for answers which deviate even slightly from the preprogrammed ones. So the question is a valid one, but not one we can answer here. The proper answer would come from whatever convention the teacher or web course designer had chosen. It's less a mathematical exercise than an exercise in the ability of students to follow received conventions.

Also $6\times 4 = 4\times 4 = 20$

 

[vela]

This is why we invented scientific notation, to avoid such confusion.

No, it is not. We invented scientific notation so as to not have to write out dozens of zeros for large numbers.

Please, you guys aren't fooling anyone. Scientific notation and sig figs were invented to confuse lay people and keep them in the dark, thus ensuring job security for the elites.

 

[malawi_glenn]

I also tell my students "sig figs are poor mans error estimation"

 

[Vanadium 50]

We invented scientific notation so as to not have to write out dozens of zeros for large numbers.

Actually, scientific notation predates zero in Western math by about 1400 years. It was the lack of a concept of zero and of positional notation that triggered it.

 

[berkeman]

Actually, scientific notation predates zero in Western math by about 1400 years. It was the lack of a concept of zero and of positional notation that triggered it.

Source?

(runs and hides...)

 

[Vanadium 50]

Archimedes came up with something very much like scientific notation in his work The Sand Reckoner - or whatever that works out to in Greek c. 200 BC. Zero and positional notation started to take root in Europe c. 1200 AD. Fibonacci was instrumental in that.

 

[Nik_2213]

Similar problems arise with basic statistics if you, your soft-ware or your 'trad' button-box use the 'wrong' algorithm to calculate eg standard deviation. Small differences between large numbers can easily trip you up.
I had a situation where my stats calculator gave a sufficiently different answer to a colleague's for a remarkably simple data-set that I just had to go digging.
I ended up generating a 'family tree' of the math cores of all the calculator variants in our labs, along with comparable results from eg Excel and a 'very long precision' package on my A410/1...
My unsettling report got us issued with a calculator version with enough internal significant figures to side-step the issue...
Another time, I got into trouble for quoting a calibrated solution's factor to 4 DP instead of our usual three. Yeah, well, the initial 3 DP factor was giving 'unacceptable' results for a product. So I kept calibrating and calibrating until it was beyond even unreasonable doubt. Still took a 'second opinion' to confirm a 'totally bullet-proof' process had suffered an implausible 'murphy bomb'....