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A can contains 375 mL of soda. How much is left after 308 mL is removed?
Question by OpenStax is licensed under CC BY 4.0.
Final Answer
$67 \textrm{ mL}$
Solution Video

OpenStax College Physics Solution, Chapter 1, Problem 16 (Problems & Exercises) (2:53)

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Video Transcript

This is College Physics Answers with Shaun Dychko. A can of soda has 375 milliliters initially so I have the subscript <i>i</i> there to denote initial volume and then there's that change in volume and this <i>Δ</i> symbol means 'change in'; a change in volume of 308 milliliters against so it's taking away 308 milliliters and I have a negative sign to represent that— you don't have to write it this way but that's the way I like to think about it. So the change in volume is the final volume minus the initial volume and that means if you wanna solve for final volume, you can add <i>V i</i> to both sides. And so the final volume is the initial volume plus this change or in other words, 375 milliliters take away 308 milliliters. This is all kind of just a complicated way of saying something obvious which is you know, the amount left is what you started with minus how much is taken away but it's useful to get used to these kinds of symbols because this delta is gonna appear a lot in your Physics course and initial and final is gonna appear a lot as well so why not. So we subtract these two and get an answer of 67 milliliters. Now the topic here is you know, precision and significant figures and so on so let's talk about that. When you are subtracting two numbers, your answer will be precise to a place value that is the same as the least precise number that you are working with. Now in this particular case, it's straight forward because they both are precise to the ones place and so our answer is also gonna be precise to the ones place; that's the ones place, the ones place and the ones place there. Had this been a bit different, let's say, 375 milliliters minus 360 milliliters, the answer might seem to be 15 however, that's technically not the right way to do it because this number is precise to the tens place, this zero is not significant when written in standard form like this; if it was, you know, 3.60 times 10 to the 2 milliliters, well then you would say, yes the zero is significant but written this way, we have to assume that it's not and so this number is precise to the tens place and so the precision of our answer should be the same as the least precise number that we are working with which is this one; it's precise to the tens place whereas this one's precise to the ones place and so our answer can be precise only to the tens place that means the answer is 20 milliliters; it would have to be rounded to just the tens place. Okay, there we go!