# Significant Figures question

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How would you answer these questions? My dd has tried numerous times, and I've tried--I can't see what's wrong. (Her classes start on Monday but the instructor assigned homework because her first lab is on Monday. It's one of those quizzes where you can retake it as many times as you want with no penalty--but I just can't see why her answers are wrong. Maybe one of you will know?)

Perform the following calculations using the convention for significant figures. Type the numerical answer followed by a space and then the unit abbreviation. Do NOT use Scientific Notation.

596000 mg / 0.023 mg = ____ (two significant figures, so she rounded up and gets 26000000 mg. She has also tried using commas--26,000,000 mg. And she has tried not rounding, even though the instructions say to round up).

0.00598 mm + .004 mm = ___ (one significant figure, so again she rounded up and gets 0.01 mm. She has also tried not rounding: 0.009 mm)

Does anyone know where we are going wrong?

I feel like it's going to be a long semester! At least after classes start, she can go to the tutoring center or her instructor will have office hours! Maybe the quiz is programmed wrong?

Appreciate any help!

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On the addition one, I do see where it says that the result should be reported to the same number of decimal places as the number with the fewest places--so, does that supersede the instruction about significant figures? (0.010 would be the same # of decimal places as 0.004, but more significant figures--that seems to make sense to my non-scientific mind! She's going to try that tomorrow. I guess she's done. Me, I want to try it now, LOL!)

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I'm wondering if she's supposed to change the units? E.g. 26,000,000 mg = 26 kg?

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I'm wondering if she's supposed to change the units? E.g. 26,000,000 mg = 26 kg?

That's something she hasn't tried (and that would make it 100% clear there are only 2 significant figures). None of the book examples changed the units but it's worth trying. Thanks!

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Found an online calculator that says 26000000 also, but it did agree with the .010 answer. So, maybe she can at least get that one! Very curious to try the 26 kg. And then have her email her instructor!

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Thinking about this more, I'm also thinking that if you have x mg / y mg, the mgs cancel each other out, and you're left with no units.

ETA: so just 26,000,000.

Edited by luuknam
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How would you answer these questions? My dd has tried numerous times, and I've tried--I can't see what's wrong. (Her classes start on Monday but the instructor assigned homework because her first lab is on Monday. It's one of those quizzes where you can retake it as many times as you want with no penalty--but I just can't see why her answers are wrong. Maybe one of you will know?)

Perform the following calculations using the convention for significant figures. Type the numerical answer followed by a space and then the unit abbreviation. Do NOT use Scientific Notation.

596000 mg / 0.023 mg = ____ (two significant figures, so she rounded up and gets 26000000 mg. She has also tried using commas--26,000,000 mg. And she has tried not rounding, even though the instructions say to round up).

0.00598 mm + .004 mm = ___ (one significant figure, so again she rounded up and gets 0.01 mm. She has also tried not rounding: 0.009 mm)

Does anyone know where we are going wrong?

I feel like it's going to be a long semester! At least after classes start, she can go to the tutoring center or her instructor will have office hours! Maybe the quiz is programmed wrong?

Appreciate any help!

I think this is the way to approach it:  The first problem is a 6 significant figure number divided by a three signficant figure number, so the answer should be a three significant figure number

For the second problem, the answer should have three decimal places (the same as the least precise addend).  So 0.00998 would be rounded to 0.010 (which is the same arithmetically as 0.01 but shows the accuracy to which the measurement is taken).

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I think this is the way to approach it:  The first problem is a 6 significant figure number divided by a three signficant figure number, so the answer should be a three significant figure number

For the second problem, the answer should have three decimal places (the same as the least precise addend).  So 0.00998 would be rounded to 0.010 (which is the same arithmetically as 0.01 but shows the accuracy to which the measurement is taken).

0.023 is only 2 significant figures though--leading zeros don't count. How do you get 3?

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Btw, I'd probably also try entering the answers without the space it tells you to put between the number and the units... because that seems like an easy mistake for the creator of the quiz to have made (either programming it wrong, or writing the wrong instructions).

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Thinking about this more, I'm also thinking that if you have x mg / y mg, the mgs cancel each other out, and you're left with no units.

ETA: so just 26,000,000.

You know, I did kind of wonder about that, but then I thought I wasn't making any sense to think that! I know to do that when converting units, but couldn't remember doing it when not converting them... Maybe you're right though!

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You know, I did kind of wonder about that, but then I thought I wasn't making any sense to think that! I know to do that when converting units, but couldn't remember doing it when not converting them... Maybe you're right though!

Like, if we have 1000 mg of sugar, and we're putting it into bags of 10 mg each, then 1000 mg/10 mg = 100. We'd end up with 100 bags. Not with 100 mg.

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0.023 is only 2 significant figures though--leading zeros don't count. How do you get 3?

You are right, it is only 2 significant figures.

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I'm not too fond of significant numbers anyway... they're nice and all, but I haven't really seen them used irl... if you read journal articles, it's all about confidence intervals and all that kind of stuff. (for example, to paraphrase Wikipedia, one of the problems is if you have 8*8=6*10^1... since you basically are multiplying something between 7.5*7.5=56.25 and 8.5*8.5=72.25, 6*10^1 implies the answer is between 55 and 65, while we know the answer could be between 56.25 and 72.25... 64 plus/minus 8 would be a more accurate representation of uncertainty (which isn't what a confidence interval is, btw... just a random explanation why significant numbers have their limitations)).

Edited by luuknam
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596000 mg / 0.023 mg = ____ (two significant figures, so she rounded up and gets 26000000 mg. She has also tried using commas--26,000,000 mg. And she has tried not rounding, even though the instructions say to round up).

The answer should not have a unit; the mg cancel.

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Does it want the answers in scientific notation? Often 2.6 x 10^7 is used to clarify the number of significant figures, and scientific notation is the first lab in a lot of intro science classes.

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Does it want the answers in scientific notation? Often 2.6 x 10^7 is used to clarify the number of significant figures, and scientific notation is the first lab in a lot of intro science classes.

It specifically states in the OP to not use scientific notation.

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The answer should not have a unit; the mg cancel.

You've reminded what did freshman year when I forgot formulas on exams. If I knew the units the answer had to have I combined the numbers in a way that would result in the correct units. Worked every time.

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You've reminded what did freshman year when I forgot formulas on exams. If I knew the units the answer had to have I combined the numbers in a way that would result in the correct units. Worked every time.

It works, unless there are numerical prefactors like 2 or pi or 4/3. Dimensional analysis won't help with those.

I always model checking units for my students and encourage them to do this on every problem.

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The answer should not have a unit; the mg cancel.

I'm also reminded of my dds high school chem teacher who shortened "formula units" to f u not "units." She wrote f u on the white board almost daily and seemed frustrated that 15 year olds were snickering every time. She was not a native English speaker.

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Like, if we have 1000 mg of sugar, and we're putting it into bags of 10 mg each, then 1000 mg/10 mg = 100. We'd end up with 100 bags. Not with 100 mg.

Ah, that's a great way to explain it, thanks!

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Thanks everyone!

yup, it was 26000000 (no label) for the one, and 0.010 mm for the other.

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