Question

Which shows the results of the conversion of 6.7249 × 10-5 grams to kilograms in three significant figures?

A.
6.70 × 10-9 kg

B.
6.725 × 10-9 kg

C.
6.7249 × 10-9 kg

D.
6.72 × 10-9 kg

Answer 1

@zepdrix

Answer 2

Wow, before my brain explodes, and I'm led away totally mesmerised, and given that there are 10^3g in a kg ...
6.7249x10-5g=>6.7249x10-8kg=>67.249x10-9kg which isn't in the list
Then I clearly don't understand this question ...
Which is a pity, because the actual idea behind the question is good, although these things are often done in "terse maths speak" = incomprehensible to an osprey.
A. 6.70 × 10-9 kg B. 6.725 × 10-9 kg C. 6.7249 × 10-9 kg D. 6.72 × 10-9 kg
If i get rid of the powers of 10, then significant figures SEEMS to boil down to "rounding things". Here, the number is - 6.7249 - closer to 7 than to 6, so you'd say "it's about 7, just a little under". So to ONE S figure it would be 7. Then, it's closer to 6.7 than it is to 6.8 which would suggest 6.7 to TWO S figures. Then, its a shade closer to 6.72 than it is to 6.73 which would suggest 6.72 to THREE S figures, and so on.
This is either right, or a complete and utter shambles, and I've fallen out of my nest/tree ??
bon chance et bon voyage
http://perendis.webs.com

Answer 3

You're right, @osprey, but goodness gracious, that's a mess of a ramble... To cut it down for you:
Point 1: A kilogram is composed of 1 x 10^3 grams.
Point 2: When converting between metric units of the same dimension, we just move decimal points and don't change numbers. In scientific notation, this means we can round to the sig figs and put the power of 10 on afterward.
Point 3: All nonzero digits are significant. That means, to 3 sig figs, we 6.7249 rounds to 6.72 (cause 4 is less than 5).
Point 4: Generally you'd add the powers of 10 next, but since they're all the same, it's obvious what the answer would be (are you sure your numbers are right? It doesn't seem as if 10^-5 is the correct value there...)
Final answer: D. 6.72 x10^-9
Make sense? Require further explanation?

Answer 4

@SapphireMoon Hi, I'm not sure that my numbers are right at all. The only real expl that I think would help is "where do I get a brain transplant from". My real problem with this sort of question is that it seems to me to obscure the point of the idea. The idea, I think, is to do "successive approximations" depending on other things in the procedure such as "cumulative uncertainties" and the like. the algebraic/arithmetic gymnastics are good "marking fodder", but to me they don't seem to "hit the point". So, why make the solver convert grams to kg, flick in a power of 10 and then doing the successive approx. or rounding ? I very strongly suspect that the solver may very well get demoralised by jumping through these hoops. Mind you if it's a question on a MATHS paper, then grim experience makes me suspect that the whole question would be worth ... 1 ... 2 marks.
Putting it a different way. I once went into a bedroom to sleep, years ago in this particular one. The bed was very, very, very neat and TIGHT !!!! It was so tight that I couldn't get into it, without almost tearing it apart !. Wooohoooo ! And a lot of what I see seems to be in that sort of vein.
I accept that the "examiners" don't make that many mistakes/typos. But, that perhaps, I desperately wondered, the poster had.
Now that I'm fallen out of my nest, I also notice that my beak's got wedged in the ground !
Have a good 'n.

Answer 5

@osprey I was referring to the poster's numbers, not yours. And it does seem a little patronizing, but then again, if you don't do those types of checks you end up with people making stupid mistakes cause they slipped through the cracks not knowing this stuff...

Answer 6

@SapphireMoon Ah, you mean you reckon that my ramble was right ? What at first sight looked to me to be a relatively simple question, firstly misread as decimal places, became something of a trip over everything in sight in the middle of a pea souper fog. And, for my money, this often picky detail just wears me out. Better, perhaps, to say that if you've got a metre rule, then you can "ideally" measure to half of the smallest scale marking - about 0.5mm if memory serves me. Notwithstanding that the "best" fractional error measurements are of things at the top end of the rule - ie long - there's no point in trying to get 0.1mm out of the thing, because it's probably not designed for that. and 0.05mm is even "sillier". So, whatever the calculator says, the number quoted should "match" the tools used to get it. Phrasing that sort of thing in a physics/maths question is, to my mind, a more instructive approach.
Ironically, at the moment I'm doing some "research" (not very posh) into the precessing orbit of mercury around the sun. The rate of precession is pretty low per pretty high number of years, but it seems that it was measurable as far back as at least the 1800s, and became calculable accurately when Einstein popped up with relativity (and probably his wife, Mileva, too).

Answer 7

@osprey Seems about right, if I'm reading it correctly... (Do you do that when you're talking, too, or is it just when typing?)

Answer 8

@SapphireMoon It depends very much on to whom I'm talking or writing, and about what. I look at it by thinking "ok, the questions are sometimes ... what's the word ... ?" But, what's behind firstly the question, then the poster of the question, and then the "interest factor". So, with the resistance wire electric fire, the amount of physics associated with it is huge, not to mention a spot of metallurgy. Since the questioner is free to totally ignore everything I post, I guess I'd rather put the information up there to give that choice. How many sources have I seen which offer "terse concise" accounts of some pretty complicated subjects ? Most of the stuff I've waded through in the books I've looked at.
I don't know if that helps answer your question. (A pretty obvious sentence, really)

Answer 9

@osprey Lol, I do it when I'm writing stories (so much so that it's basically become a quirk of the narrator) but I can usually control it when I'm talking to real people. (Nice talking to you, btw. Continue off thread?)

Answer 10

@SapphireMoon And to you also. Yes, that would be good. What are sapphires made of (probably asked that before) - I "know" the moon is made of green cheese, with a smiley face in it somewhere.

Answer 11

@SapphireMoon I thought of the enclosed txt in the interim between this set of postings. Possibly the usual verbiage .. I don't know ...
Bon voyage a vous