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For instance, say I have a roll of quarters and a roll of dimes. I can use the dimes and quarters in a parking meter, but 50 cents in dimes gets me less time than 50 cents in quarters. Additionally, I can't even use dimes in the washing machine and dryer in my apartment, but I can use quarters. So even though both 50 cents in both dimes and quarters are worth 50 cents, quarters clearly have a higher "meta-value", if you will, thus making them worth more.

I'm new to economics and am unsure how to Google this question.

kol
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    You've correctly tagged the question [tag:utility], which is the answer to your question. Read more here – 410 gone May 19 '15 at 07:20
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    But given that you can exchange the dimes for quarters without cost, at least in principal, I'm not sure it makes sense to define values other than their face values. The only application I could imagine is an optimization problem where, given a fixed budget (say ten dollars), you have to decide how many of each coin (with their uses as defined in your question) to have such that their face values sum to your budget. Of course, given how you've defined the uses above, the answer is trivially all quarters. – Shane May 19 '15 at 14:18

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