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I have $x = 100$. I need to get a range that is plus/minus $10\%$ of $100$.

That means in my case $x=100$:

  • $10\%$ of $100$ = $10$
  • $100 - 10 = 90$
  • $100 + 10 = 110$

That means my range of $100 \pm 10\%$ is: $90 - 110$

Correct?

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2 Answers 2

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Yes, that is correct............

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Yes it is correct. Do you want a curious fact? You have $100$, you add $10\%$ and you have $110$. Then you take away $10\%$ (that now is worth $11$) and you end up with $99\%$. After adding and afterwards deducting the same $10\%$, you lose $1\%$.

Bad luck? Let's try reversing the process. Start again with $100$ but this time start subtracting $10\%$, so you have $90$. Now add $10\%$ of that and you have... $99$ again!

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  • $\begingroup$ Don't confuse the op with the "curious fact." What you describe shouldn't be surprising anyways since the 10%'s are not 10% of the same quantity. $1.1\cdot 0.9\neq 1$. $\endgroup$
    – JMoravitz
    Commented May 13, 2017 at 21:27
  • $\begingroup$ I don't think this is confusing. Maybe it is "warning". Some people might be seriously surprised (if not disappointed) if they find themselves with assets not fully recovering their value after after reading on the newspapers one day -10% and the day after +10%... $\endgroup$
    – lesath82
    Commented May 13, 2017 at 21:46
  • $\begingroup$ Does this phenomenom have a name? $\endgroup$
    – Worthy7
    Commented Jun 23, 2021 at 17:00
  • $\begingroup$ @Worthy7 Not one that I'm aware of $\endgroup$
    – lesath82
    Commented Jun 27, 2021 at 8:57

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