Hi everyone today I took a Chemistry quiz it had only 1 question. The question had 3 different distances of miles (They all had 5 significant figures, I can’t remember the numbers) and it said a person wastes 27 gallons per mile (27 has 2 significant figures). 1 gallon is about 2.583$ (I can’t remember the exact number) (2.583$ has 4 significant figures) What is the amount of dollars the dude has to spend on gallons of gas?
So what I did was I added the 3 different distances of miles together and got a number in miles. Then I divided it by 27 since gallons per mile. Then I multiplied by 2.583 and got 55.4615280578$.
So what we have here in the question is:
27 Gallons (2 Significant Figures)
3 Different Distances Of Miles (Each number has 5 significant Figures)
2.583$ (4 Significant Figures)
So what I did was round 55.4615280578$ to 4 significant figures since we have that number in dollars and we should round to 4 significant figures since $2.583 has 4 significant figures and they’re both in dollars. So I put 55.46$ as my answer.
It turns out the answer is 55.461$…?
The teacher said we round to the number of significant figures in miles which is 5 significant figures.
So the answer would be 55.461$ not 55.46$.
So I got my quiz back and got a 0. My question is why do we round to 5 significant figures and not 4 significant figures. We can’t really have 55.461$? You can’t pass the hundredths place when talking about money in cents. Also I thought you’re supposed to round the significant figures according to the units so 55.4615280578$ is in dollars and 2.583$ is also in dollars so you round to 4 significant figures to get 55.46$, but that’s wrong?
Also what would be the answer if the first distance had 3 significant figures, the second distance had 6 significant figures, and the third distance had 5 significant figures? Assuming the final answer is still 55.4615280578$.
Thanks! I hope you’re not confused by reading this, I’m just depressed that I got a 0… I need a 93 in the class to get a 4.0 but this quiz will for sure drop my grade and I’m scared I’ll mess up on the exam.
Honestly I would use two significant figures since 27 only has two (as opposed to 27.00 mpg), but rounding to the nearest cent makes sense to me here. I don’t understand why he insists five.
So what I did was I added the 3 different distances of miles together and got a number in miles. Then I divided it by 27 since gallons per mile. Then I multiplied by 2.583 and got $55.4615280578.
If what you said here is exactly true, then your answer is $55 because 27, with two significant figures, limits the final answer. Some teachers, like the one you might have, are very, very bad.
I’m a former chemistry teacher. I agree with 1golfer1. You always use the least number of sig figs which was 2 (from 27) Were the units for 27 - gallons/mile or miles/gallon? If you got the units wrong, that would account for the zero.
The only thing I can think is that the fuel cost (dollars/gallon) and the vehicle fuel “wastage” are exact numbers. If that’s the case, then your answer should be expressed in the same significance as the measurements which were 5 figures.
My teacher said something about having an infinite possibility of sig-figs when doing Dimensional Analysis like above. So you pick a certain number (but that’s what I am trying to find out, which number am I supposed to pick?) and round it based on the number of sig-figs in that number. And it was 27 Gallons per mile and I asked my teacher why I got a 0, it wasn’t for the units it was for the sig-fig rounding.
That’s because this entire question is about sig-figs. The math and the logic is unimportant. If 27 gallons per mile was an exact number, then the significance of the answer is indicated by the measurements. That’s the take home lesson.
I’ve made the same mistakes before, and I have to say the teacher was justified here. If the starting value was just 27 gpm, then the resulting answer even after DA should only have 2 SF.
27 GPM (are you sure it’s not MPG? The units don’t work out right if it’s GPM) should never have infinite significant figures. It’s not a proportion or some constant derived from basic principles. It’s a measurement. The whole point of using significant figures is to accommodate for the fact that measurements are imprecise.
Since all of the operations are multiplication, the rule to follow is that the answer has the same number of sig figs as the least significant measurement, in this case 2 sig figs. The answer should be $55.
There is no way for the answer to have 5 sig figs, even if the 27 MPG measurement had infinite sig figs, because there is a measurement that contains less sig figs (2.583 dollars/gallon).
Anyways, I think it’s unduly harsh to give you zero credit for getting the sig figs wrong. If I were grading I would give you 3/4 of the credit (1/2 for showing work and performing the correct operations, 1/4 for getting the right number).
This is what my Chemistry teacher said when I asked her through email:
“The final answer should always be rounded based on the number of significant figures in the given measurement, which in the case of the quiz question, is the distance traveled. The price of gasoline is used as a conversion factor and is assumed to have infinite significant figures.”
Turns out I got a 20 because I showed some of my work on it; partial credit. (I should’ve showed ALL of the work since I put most of it in my calculator)
Four of your threads have been complaining about tests or teachers. I suggest that you just work hard and do your best. If you go into college with a negative attitude about professors and exams, you’re going to have a hard time. You’re not going to get special treatment in college.
I’m confused how you would assume the price of gasoline has infinite sig figs…
Also, isn’t science based on theories and laws, not assumptions? My chem teacher said a lot of chem is theoretical since we can’t see and measure a lot of microscopic things directly, but nothing has been to disprove certain things but it’s not based on assumptions…