Is my electronic textbook incorrect?

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Discussion Overview

The discussion revolves around the interpretation of a textbook statement regarding the calculation of percent yield in chemistry. Participants examine whether the use of "100%" in the context of multiplying a fraction is correct or if it should simply be "100." The scope includes conceptual clarification and technical reasoning related to percentage calculations in chemistry.

Discussion Character

  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant asserts that multiplying anything by 100% will yield the same number, suggesting the authors intended to write 100 instead of 100%.
  • Another participant agrees that the fraction representing yield should be less than 1, indicating that the textbook may contain errors that are often corrected in later printings.
  • A different participant reflects on their initial understanding, providing an example calculation of percent yield and questioning the inclusion of 100% in the equation.
  • One participant argues that the textbook is correct, explaining that multiplying by 100% is necessary to convert a decimal to a percentage, emphasizing the importance of the percent sign as a unit.
  • Another participant acknowledges both notations (multiplying by "100" and "100%") but finds the latter to be ambiguous, noting that multiplying by 1 does not yield the correct percentage answer.

Areas of Agreement / Disagreement

Participants express differing views on the correctness of the textbook's notation. Some believe it is incorrect, while others defend it as acceptable. The discussion remains unresolved regarding the appropriateness of using "100%" versus "100."

Contextual Notes

Participants highlight potential ambiguities in the notation and the implications of using different forms of expressing percentage calculations. There is an acknowledgment of the need for clarity in mathematical expressions related to percent yield.

Qube
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Is it just me, but if you multiply anything by 100% you'll end up with the same number?

I believe the authors meant to write 100, not 100%.

This is from 5 steps to a 5 AP Chem.
[PLAIN]http://i.min.us/icDcjc.png
 
Last edited by a moderator:
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Qube said:
Is it just me, but if you multiply anything by 100% you'll end up with the same number?

I believe the authors meant to write 100, not 100%.

Welcome Qube to PF Forums!

Yes you are correct. The fraction will always be less than 1 because actual yield will never exceed theoretical yield. If it does, this is good chance an error was made either in the experiment or calculations. So to express as a percentage you multiply by 100 (not 100%). Textbooks can have errors in them, they are usually fixed by the 2nd or 3rd printing.
 
Now that I think about it, I believe I am in error.

Suppose the actual yield was 50g, and the theoretical yield was 100g.

50% = (50/100) * 100%

50% = .5 * 1

50% = .5

I still wonder why they left the 100% in though ...

And multiplying .5 by 100 as I proposed would yield 50. 50 does not equal 50%, but the left side of the equation clearly states "% yield."

[PLAIN]http://i.min.us/icDcjc.png
 
Last edited by a moderator:
Hi Qube,

The textbook looks fine to me.

Think of the percent sign as a unit. If I want to convert .5 to percent, multiplying by 100 will only give me 50, which only means that I multiplied .5 by 100. If you want to convert .5 to a percentage, multiply .5 by 100% and you'll get 50% which is the desired result.

Qube said:
And multiplying .5 by 100 as I proposed would yield 50. 50 does not equal 50%, but the left side of the equation clearly states "% yield."

Exactly what I'm thinking. The left side of the equation says % yield, which means you'll need a percentage sign on the right side.
 
gb7nash said:
If I want to convert .5 to percent, multiplying by 100 will only give me 50,
Actually you get 50% because it is given you are calculating % yield.

I have seen both notations, multiplying by "100" and "100%." but I find the later
to be ambiguous. A valid interpretation (as qube noted) 100% = 1, but multiplying
by one does not give you the correct answer as a percentage.
 

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