Significant Figures and other basics in a Chemistry for Engineers class

[ceri23]

I'm hoping for verification here that I'm not crazy on some very very basic chemistry questions. I've worked 7 problems on a practice test (the real thing is next Tuesday). Only 2 of my answers agree with the answer key. Here are the most dramatic examples. Please tell me I'm not crazy.

Homework Statement

Four very basic problems:
Problem 1:
[(1.900 + 0.0200) / (23.75 + 0.25)] + 0.06223 = ?
a.) 1
b.) 2
c.) 3
d.) 4
e.) 5

Problem 2:
2.94 x 10-6 + 5.118 x 10-5 + 8.80 x 10-7
a.) 5.5 x 10^-5
b.) 5.50 x 10^-5
c.) 5.500 x 10^-5
d.) 5.5000 x 10^-5
e.) none of these

Problem 3:
How many picograms are in 275 ug (micrograms)?
a.) 2.75 x 10^8 pg
b.) 2.75 x 10^-4 pg
c.) 2.75 x 10^5 pg
d.) .275 pg
e.) 2.75 x 10^8 pg

Problem 4:
Which of the following correctly pairs the physical quantity with the SI unit associated with it?
I. Volume, L
II. Mass, kg
III. Temperature, *C

a.) I
b.) II
c.) III
d.) I and II
e.) II and III

Homework Equations

None

The Attempt at a Solution

I've been forced to retake an intro level chemistry class for engineers (degree plan problems to graduate). I thought I was done with sig figs. I'm studying for the first major test and I'm 100% on everything except these three problems with sig figs and basic prefixes.

Problem 1 attempt:

Applying the rules one step at a time:

Numerator: 1.900 + 0.0200 = 1.9200 truncated to 1.920 (by place)
Denominator: 23.75 + 0.25 = 24.00 no truncation (by place)

So reducing I'm left with:
(1.920 / 24.00) + 0.06223

Performing the division: (1.920 / 24.00) = 0.0800000000 truncated to 0.08000 (4 places by number of digits for multiplication and division)

Reducing down:
0.08000 + 0.06223 = 0.142230000 truncated to 0.14223 (by place)

This suggests my final answer has 5 significant figures. The answer from the answer key is 3 sig figs. I can't purposely work this problem incorrectly and come up with 3 sig figs.

Problem 2 attempt:

Just writing them out longhand (instead of scientific)

.00000294
.00005118
.000000880
__________
.000055000 truncated by place to .00005500, and converting to scientific notation (as the answers are listed) I have 5.500 x 10^-5. The correct answer is listed as 5.50 x 10^-5.

Problem 3 attempt:
micro is 10^-6. pico is 10^-12. So there are 6 places without messing with the decimal. Slide the decimal over 2 more places to arrive at 2.75 x 10^8. The correct answer is listed as 2.75 x 10^7.

I'm a little weaker on sig figs since I haven't used them since taking gen chem 5 years ago, but I'm virtually certain this answer is wrong. I've been using these prefixes for junior and senior level classes for 2-3 years in electrical engineering. Problem 3 makes me call the whole answer key into question.

Problem 4 attempt:

I and II. Answer key says only I. Volume is liters. Mass is kilogram. Temperature is kelvin. Does chemistry treat mass as grams instead of kilograms? Is this some special exception or was this test written in a hurry? I'm tearing my hair out over these.

 

[mfb]

That is a weird test.
In (1), the 5th digit is nearly meaningless, so 4 significant figures might be better than 5. I don't understand how you get 3, unless you remove one digit for the fraction, too.

I think (2) uses the same concept, and drops the last digit.

(3): You listed the correct answer (^8) twice.

(4): Technically, kg is derived from the g (1kg=1kilogram=1000gram). At the same time, it is the SI base unit, so I think it is correct.
Volume, on the other hand, is length cubed, without its own base unit. m^3 is the "easiest" way to get a volume with SI base units. Liter is NOT an SI unit!
=> II is correct, I is not.

 

[ceri23]

That is a weird test.
In (1), the 5th digit is nearly meaningless, so 4 significant figures might be better than 5. I don't understand how you get 3, unless you remove one digit for the fraction, too.

I think (2) uses the same concept, and drops the last digit.

(3): You listed the correct answer (^8) twice.

(4): Technically, kg is derived from the g (1kg=1kilogram=1000gram). At the same time, it is the SI base unit, so I think it is correct.
Volume, on the other hand, is length cubed, without its own base unit. m^3 is the "easiest" way to get a volume with SI base units. Liter is NOT an SI unit!
=> II is correct, I is not.

You've hit on all the same problems I have with these questions. They're so basic and virtually insignificant later on that they're "hard".

(1) The purpose of the question isn't about what's practical. It's about what's "right" according to the rules of significant figures, so as far as dropping trailing zeros, they're considered "important" for a question like this.

(2) Same

(3) Sorry, yeah. ^8 is certainly right.

(4) You said that liters aren't an SI unit? I thought it was a derived unit, but still considered an official SI unit of volume. Force for instance is the Newton, but that's a derived unit of kg*m/s^2.

The reason I'm asking here is for confirmation that I'm not crazy. I'm pretty sure I know these answers, but the answer key is goofed pretty bad. I'm trying to arm myself for an email to the prof about how backwards this practice test is (with very kindly worded sentences), especially since students are going to be using it to solidify this material.EDIT: Aaaaand as soon as I posted this I checked my school email and the prof announced that there are a bunch that are wrong on the old practice test. Thanks for the reply mfb. I tore my hair out for 3 hours last night over this crap before posting here.

 

[mfb]

It's about what's "right" according to the rules of significant figures

I would say the whole concept of significant figures is not "right". It is a quick way to estimate the order of magnitude of the uncertainty, with the assumption that the given parameters use the same method. It is not a proper uncertainty analysis.

(4) You said that liters aren't an SI unit?

Right. They are accepted to be used together with SI units, but they are not an SI-unit.
An SI-unit for the volume would have the value of 1m^3.

EDIT: Aaaaand as soon as I posted this I checked my school email and the prof announced that there are a bunch that are wrong on the old practice test.

Oh, good.

 

[DeeNos]

I can confirm that your answers for problems 1, 2, and 3 are correct. It seems like the answer key may have some errors or inconsistencies. It is always important to follow the rules of significant figures and unit conversions in chemistry, and your approach to these problems is correct. As for problem 4, the SI unit for mass is indeed kilogram, so your answer of I and II is correct. It is possible that the answer key meant to say "grams" instead of "kilograms" for mass, but it is best to confirm with your instructor about this. Overall, it is important to trust your knowledge and understanding of these basic concepts in chemistry, and don't be afraid to question the answer key if you believe it may be incorrect. Good luck on your test!