the numbers aren't working nicely

[Addallat]

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TBR example 3.7 on page 171

the explanation of the calculation of the equilibrium constant in TBR states the following "the numbers work nicely" in determining the equilibrium constant and lists:


(0.275/.225)^3 = (11/9)^3




Can someone explain to me how you're supposed to know off the bat that .257/.225 = 11/9?

To be honest once I got at this point in the question I just wrote out the math of .257/.225 and saw that it was 1.2 solving the problem from there easily. It probably would have saved me a few seconds if I would've known .275/.225 = 11/9.... but I guess every second counts on a timed test so I'm curious to see if someone can explain the above and make me more efficient at solving the problem. ty

 

[dudewheresmymd]

This is just arithmetic...comes with practice, basically just multiplying and dividing by different forms of 1.

.275/.225 (multiply both num and denom by 1000) =275/225 (both end in 5 therefore divisible by 5, divide both num and denom by 5), 55/45 (divide both num and denom again by 4) = 11/9, that's how I would have done it.