[Elric82]

I have been studying chemistry for awhile now. Started off with the interesting stuff (organic), and have learned quite a bit. When there was something I didn’t understand I would look up the concepts and study them. I am not a student, but would like to go to the local university some day soon (I’m almost 35). That being said, I’ve decided to take one of my text books and start from the beginning.

I came across a simple question: If the density of milk is 1.04g/ml,
how many grams of milk are in 0.50qt of milk? Here is what I did:

0.50qt x 946ml/1qt = 473ml x 1.04g/1ml = 491.92g

I rounded this to 492g. Textbook answer was 490g (4.9x10²⁾.  This “small” discrepancy keeps popping up on different problems. I think my problem lies in sig figs. Am I correct in my assumption about the problem being in the use (or lack thereof) of sig figs?

The textbook solved it like this 0.50qt x 1L/1.06qt x 1000ml/1L x 1.04g/1ml = 490g

[Corribus]

The book's conversion factor of qt to liter is slightly different than yours...

[Elric82]

The book's conversion factor of qt to liter is slightly different than yours...

That’s not a good, seeing how all conversion factors came from the same textbook. The book is : “Chemistry An introduction to General,Organic, and Biological Chemistry” tenth edition, written by Karen C. Timberlake.

[Arkcon]

I rounded this to 492g. Textbook answer was 490g (4.9x10²⁾.  This “small” discrepancy keeps popping up on different problems. I think my problem lies in sig figs. Am I correct in my assumption about the problem being in the use (or lack thereof) of sig figs?

I think that is part of the problem.  The purpose of significant figures is that your calculated accuracy can't be claimed higher than your measured accuracy.

Given:

Here is what I did:

0.50qt x 946ml/1qt = 473ml x 1.04g/1ml = 491.92g

And you have two significant figures for the measured value of quarts.  So you answer should have two significant figures, or 490 g

I rounded this to 492g. Textbook answer was 490g (4.9x10²⁾.  This “small” discrepancy keeps popping up on different problems. I think my problem lies in sig figs. Am I correct in my assumption about the problem being in the use (or lack thereof) of sig figs?

Part of the problem, yes.

Now given:

The textbook solved it like this 0.50qt x 1L/1.06qt x 1000ml/1L x 1.04g/1ml = 490g

so, combining the middle terms, to make the calculation  more like yours:  1000ml/1.06 qt =943.40 ml

 0.50 qt x 943ml * 1.04 g = 490.36g

Which again, we would round to 2 significant figures, for 490 g

The book's conversion factor of qt to liter is slightly different than yours...

That’s not a good, seeing how all conversion factors came from the same textbook. The book is : “Chemistry An introduction to General,Organic, and Biological Chemistry” tenth edition, written by Karen C. Timberlake.

I don't think that's a real problem.  The 946 mL you use for ml in a US quart is not much different than the 943 g/US quart the second one uses.

[Elric82]

Thanks Arckon. I read you’re reply the other day, but I had consumed a fair amount of beer by then unfortunately. Looking at it after I got off work, and flipping back through the text, I found that the sig figs in conversion factors are restricted to what is MEASURED.
Which would be the 0.50 qt’s. Which you posted in the reply. Again,
thank you. I was beginning to think the back of the book was easier
than the front. I looked at it both ways, and you get the same answer when you follow the rules stated before hand. Lesson learned
( I hope).