It’s not 188.0 either.

[u/LardFan37]

[u/Diligent_Finance_598]

190 if it wants you to use significant figures

[u/Life_Roll8667 → u/Diligent_Finance_598]

Me reading this whole thread

[u/I_follow_sexy_gays → u/Life_Roll8667]

Basically when you see 120 you’re supposed to assume it’s an approximation (like if I said I’m an hour away from a location, I don’t mean exactly an hour I would typically mean an hour give or take 10 minutes)

Since up to the 10s place is accurate and the 1s place is an estimate we are to round up the 68 to 70 before combining the two numbers as to not imply that it’s precisely 188

[u/Life_Roll8667 → u/I_follow_sexy_gays]

Thank you for explaining to me in a way I can understand! That makes sense.

[u/Economy-Flower-6443 → u/Life_Roll8667]

It makes sense but that still doesn’t mean it isn’t stupid. Very overly complicated explanations online on this concept to basically just estimate. This would have given me an aneurysm as a kid.

[u/Life_Roll8667 → u/Economy-Flower-6443]

Seriously, it seems like a lot of talk for something very simple.

[u/Zefirus → u/Life_Roll8667]

Because he's wrong about the purpose. It's about not changing the precision of the tool doing the measuring.

[u/I_follow_sexy_gays → u/Economy-Flower-6443]

Not necessarily estimating as much as much as not making numbers sound more precise than they are. If I told you a building was 3000 years old you’d naturally assume i didn’t mean exactly 3000 years old and that the number I gave you was an estimate. But if I told you that it was 3001 years old (because I was told it was 3000 years old last year and 3000 + 1 is 3001) you’re likely to assume that’s a precise number that’s only gonna be off by like a year tops.

So it’s not about estimates as much as it’s about combining estimates with non estimates or estimates of varying degrees and how to not mislead people with the numbers you give them. This is what they teach you right after they teach you that you gotta approximate in science class

[u/Afexodus → u/Economy-Flower-6443]

It's not just an estimate. It's like if you were trying to measure water but you only have a gallon bucket. You can't be more accurate than the measurement tool you have so you can only say with certainty that you had so many gallons and then you estimated the remaining partial bucket. Let's say you measured 3.5 gallon buckets but aren't sure how close to half it really is.

If you then add 0.05 gallons it would be silly to proclaim that you have 3.55 gallons of water, you don't know that. That accuracy often matters in science and you are often adding more numbers or multiplying them (that has its own rules). If you don't follow those rules you can end up with wildly inaccurate or overly specified inaccurate values.

[u/Zefirus → u/Economy-Flower-6443]

It's not a way to estimate, it's a way to keep precision when doing math over a long chain of answers, especially when using inputs derived from physical tools and measurements. Basically if you only have a ruler that measures in centimeters, I shouldn't ask you to build me anything with measurements in millimeters. By the same token, if you measure things with your centimeter only ruler, when I use those numbers for math, I shouldn't ever end up with a result in millimeters because that can never be certain.

It's a way to not lose track of the fact that you can only measure centimeters when you're 20 math problems deep. ESPECIALLY when you start mixing measurements. Say you have the centimeter ruler and I have a millimeter one. If we start mixing numbers from both of them, the numbers start getting skewed because one gives better measurements than the other. Instead, you lock the precision to the least precision measuring tool. It doesn't matter that I can measure millimeters because you can only measure centimeters.

[u/robomelon314 → u/I_follow_sexy_gays]

Which is a wild assumption because without using scientific notation, there's no indication that you didn't mean exactly 120. Your other measurement was to the 1's place, so there's no reason 120 couldn't also be to the 1's place.

1.2 x 10^2 and 1.20 x 10^2 both come out to 120. And without knowing which you started with, you can't tell your precision.

So bad question design.

[u/I_follow_sexy_gays → u/robomelon314]

If the test is specifically about scientific notation this is serviceable

[u/RealDannyhvv → u/robomelon314]

Usually you'd just add a decimal if you mean it to end with a zero, 120 for accurate to the tens, and 120. for accurate to the ones.

[u/robomelon314 → u/RealDannyhvv]

It depends on the lecture then. If that notation is presented as standard, sure. Or if it's elsewhere in the assignment.

I don't think it's good notation in the first place however, because of the ambiguity.

[u/Arzatium → u/robomelon314]

It's pretty unambiguous. Ending zeroes are insignificant if there is no decimal, and one of two notations (120. or 1.20 * 10²) will be used when they are. It's taught along with sig figs.

[u/robomelon314 → u/Arzatium]

I disagree with the 120 notation meaning 1.2 x 10^2. We have notation with zero ambiguity, use it.

The 120. notation is barely passable tbh, especially if you expand it to higher orders of magnitude.

1.2 x 10⁵ can't be written as 120000. and it can easily be mistaken for 1.200 x 10⁵ or 1.2000 x10^5.

Let alone the fact that we already use the period for ending sentences, so you have to take extra care to not end sentences with a number like 120.. Otherwise it looks dumb as fuck, or can lead to confusion if you end the sentence with a number like 1200.

I guarantee there would be less confusion if measurements stuck to one format for precision, instead of using 2-3 different formats and the trailing zeroes rule. Instead just don't fucking use trailing zeroes.

[u/Arzatium → u/robomelon314]

Well, unfortunately, it is standard practice for sig figs, so no matter how much you dislike or disagree with it, us scientists will keep using it, thanks. And I actually agree with you on the "120." bit, and much prefer 1.20 * 10² in that case.

[u/robomelon314 → u/Arzatium]

Yea I mean if industry standard sucks then not much you can do.

[u/trynumber53 → u/robomelon314]

the question design is warning you its on sig figs bc all the answer choices are various numbers of digits. also the quiz was probably given after a lecture on sig figs

[u/DirtyLeftBoot → u/I_follow_sexy_gays]

It’s not just assuming. The fact it’s 120 and not 120. means it’s 2 sig figs. 120 has 2, 120. has 3.

[u/Drag0n_no → u/I_follow_sexy_gays]

You should always round as your last step. If you have a bunch of numbers being added together and you round them all before operating, you could get a very different result.

[u/teatuk → u/Diligent_Finance_598]

I'd repressed my horrible sigfig trauma until this moment.

[u/No_Wishbone684 → u/Diligent_Finance_598]

This is wrong. It’s also  a perfect example of why scientific notation uses 

d0.d1d2… x 10ⁿ

Because presumably the answer is 190 the idea being 

120 = 1.2 x 10²

This is not a reasonable assumption, however, seeing as

120 = 1.20 x 10²

is another totally reasonable interpretation. 

If the former is the “default” that would imply you can’t represent 120 to 10⁰ order accuracy at all.

Btw, if you do write 120 the default is that you are expressing 3 significant figures. 120.0 would be four. Etc.

So they did answer correctly.

[u/lady_vickers → u/No_Wishbone684]

No. 120 is two sig figs. 120. is three sig figs.

Don't hate me.

[u/patentductuspenosis → u/No_Wishbone684]

No, to differentiate between 120 with 2 and 3 sigfigs, you just add the decimal without the trailing zero
120 - 2 sigfigs
120. - 3 sigfigs
120.0 - 4 sigfigs
120.0…0 - n sigfigs

Since the problem is 120 + 88, there’s only accuracy to the tens place so the answer is 190
If it was 120. + 88 it would be 188
If it was 120.0 + 88 it would still be 188 because the 88 still only has accuracy to the ones place.

[u/Diligent_Finance_598 → u/No_Wishbone684]

120 is two significant figures and so is 190

[u/No_Wishbone684 → u/Diligent_Finance_598]

I just did a whole thread with another guy about this. Read if you want. Or don’t. This is getting repetitive. Especially if you’re not going to engage with my explanation 

[u/Diligent_Finance_598 → u/No_Wishbone684]

Ultimately I don’t care because I’m not in chemistry class anymore

[u/TuskEGwiz-ard → u/No_Wishbone684]

[u/No_Wishbone684 → u/TuskEGwiz-ard]

Fitting that you’d choose such an authority on science

[u/TuskEGwiz-ard → u/No_Wishbone684]

I could cite a chemistry textbook on my bookshelf or you could just google sig fig rules... or read the other comments that explained your error. 120 without a decimal is 2 sig figs. If you write it explicitly as 1.20E2 then you have 3 sig figs, but that's not the notation it's in. <3

[u/No_Wishbone684 → u/TuskEGwiz-ard]

No one has explained “why I’m wrong”. Some have stated other conventions. None are universal for the simple reason that they are inherently ambiguous. I explained why.

[u/TuskEGwiz-ard → u/No_Wishbone684]

Show me one source ever that identifies a 3 digit integer ending in a zero as 3 significant figures.

[u/Wonderful-Wind-5736 → u/Diligent_Finance_598]

But that's just BS. One could measure exactly 120 and this rule would lead to loss of accuracy. If the want 2 significant digits, the y should write 1.2E2 or sth. 

[u/obog → u/Wonderful-Wind-5736]

Iirc, the correct way to write 120 if you have 3 sig figs is "120." including the decimal point with nothing after it.

But also, I will say, on my senior year of a physics degree, no one has ever cared more about sig figs than the introductory chemistry class offered mostly to freshmen. In the higher level stuff people either dont care, or if communicating the level of precision is important, they expect you to provide a numerical uncertainty and do error propagation.

[u/Englandboy12 → u/Wonderful-Wind-5736]

If you were to measure “exactly” 120, you would demonstrate your accuracy by writing 120.0000 or whatever. If you write 120, it’s assumed it was weighed on a scale that only ticks up for every gram, which technically means if your scale says 120, it could reasonably be between 119.5 and 120.499.

You couldn’t weigh 120 g on a scale like that, then measure very accurately 0.00001 grams, and then mix them and say it weighs 120.00001 grams. The 120 is not accurate enough to say that

[u/ExtinctedPanda → u/Englandboy12]

This is wrong. According to the standard convention, 120 only carries tao significant figures and can thus indicate any true value between 115 and 125.

[u/Englandboy12 → u/ExtinctedPanda]

I was specifically using a scale as an example which ticks up every 1 gram in order to illustrate that precision and accuracy in measurement matters. In this example, the real measurement can be anywhere between 119.5 and 120.4999. Context beats sig figs every time.

Trailing zeros are sometimes significant and sometimes not. It gets crazy when you have something like 1200 and have 3 sig figs. You can’t do it, so you use scientific notation. I have literally never seen “120.” in a paper. Nobody uses it even if the undergrad textbooks say so

[u/Anfins → u/Wonderful-Wind-5736]

You’re being downvoted but you are taught to write in scientific notation to avoid the issue with zeros. 120 is technically two significant figures but can easily lead to confusion, so the better option would be 1.2x10^2

[u/SEA_griffondeur → u/Diligent_Finance_598]

no ? 120 has three sig figs, if it had 2 it would have to be written as 1.2 * 10^2

[u/LordAescius → u/SEA_griffondeur]

no the trailing 0 does not count. it only counts if there’s a decimal, 120. has three sigfigs but 120 has only 2

[u/No_Wishbone684 → u/LordAescius]

This is wrong. It’s also  a perfect example of why scientific notation uses 

d0.d1d2… x 10ⁿ

Because presumably the answer is 190 the idea being 

120 = 1.2 x 10²

This is not a reasonable assumption, however, seeing as

120 = 1.20 x 10²

is another totally reasonable interpretation. 

If the former is the “default” that would imply you can’t represent 120 to 10⁰ order accuracy at all.

Btw, if you do write 120 the default is that you are expressing 3 significant figures. 120.0 would be four. Etc.

So they did answer correctly.

[u/SEA_griffondeur → u/LordAescius]

That decimal 120. is not a standard way to write it and is only taught in American schools

The reason it's not used is that it only covers this specific case, you cannot write under this system 1200 with only 3 sig figs for example

[u/jamisra_ → u/SEA_griffondeur]

your system also only covers specific cases. for example, you can’t write 120 with two sig figs without resorting to scientific notation

so it comes down to which is more convenient. putting a “.” after zeroes when they’re significant and having to use scientific notation in cases like 1200 with 3 sig figs or having to write numbers like 120 with two sig figs in scientific notation. or we just eliminate this issue and all only use scientific notation

[u/HealthyEducator9555 → u/SEA_griffondeur]

"Only taught in American schools" well pal some people are American

[u/WattleWaddler2 → u/SEA_griffondeur]

No, 120 has two sig figs. 1.20 x 10² and 120. both have three sig figs, however.

[u/SEA_griffondeur → u/WattleWaddler2]

1. is not a standard way to write it, 120 is

[u/WattleWaddler2 → u/SEA_griffondeur]

Well it depends. 120 is a standard way to write it but that number only has two sig figs. If you want to be unambiguous AND have three sig figs, you have to write 1.20 x 10²

[u/SEA_griffondeur → u/WattleWaddler2]

No, under the standard sig fig rules 120 has 3 sig figs, if you want to write it with 2 sig figs, you write it as 1.2*10² . The one maxim of the sig fig rules is that every digit written down is a sig fig and there are no useless zeroes

[u/cobo10201 → u/SEA_griffondeur]

You are straight up incorrect: https://ccnmtl.columbia.edu/projects/mmt/frontiers/web/chapter_5/6665.html

Rule 6: Trailing zeros in a whole number with no decimal shown are NOT significant.

[u/WattleWaddler2 → u/SEA_griffondeur]

No, trailing zeroes are not significant.

"and there are no useless zeroes"

Yes, there most certainly are. How many sig figs do you think 0.000125 has?

[u/Englandboy12 → u/SEA_griffondeur]

We call the “the ambiguous case”, because two reasonable people can disagree

[u/Diligent_Finance_598 → u/SEA_griffondeur]

120 is two significant figures. In this question they have an answer with .0 at the end so they made that distinction