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This confuses me a bit:

$X = 100$

Multiplying in two steps :

$100\cdot1.1 = 110$
$110\cdot1.1 = 121$

Directly multiplying by $1.2$ ($20\%$) :

$100\cdot1.2 = 120$

Angelo
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Black
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    Because $.1\cdot .1\neq .1+.1$ – QC_QAOA Dec 07 '22 at 16:37
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    Why should it be the same? Also, this is $x\cdot 110%\cdot 110%$ as opposed to $X\cdot 120%$ – JMoravitz Dec 07 '22 at 16:37
  • If you add $10$% to some positive value and then do this again, you add $10$% of a larger value at the second time. – Peter Dec 07 '22 at 16:38
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    The amount it increased by "in the second step" when "multiplying in two steps" was based on the current amount which is not the original amount. – JMoravitz Dec 07 '22 at 16:38
  • Following the first binomial formula it is $(1+0.1)^2=1^2+2\cdot 1\cdot 0.1+0.1^2$=$1.2+0.01$ This should explain the extra $0.01$. – callculus42 Dec 07 '22 at 16:39
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    Black, multiplication tag is $\text{$\cdot$}$. For example : $\text{$100 \cdot 1.1 = 110$}$. – Angelo Dec 07 '22 at 22:21
  • @QC_QAOA, actually, you should have written that the reason is that $,(1+0.1)!\cdot!(1+0.1)\neq1+(0.1+0.1),$. – Angelo Dec 07 '22 at 22:26

1 Answers1

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$x\cdot1.1\cdot1.1=x\cdot(1.1\cdot1.1)=x\cdot1.21\neq x\cdot 1.2$
multiplication is associative.
alternatively, in words: multiply the first $1.1$ get $1.1x$, multiply the second $1.1$ it is adding $10\%$ of $1.1x$ towards $1.1x$ but not $10\%$ of $x$ towards the $1.1x$, hence different.

Angelo
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Siu Zong
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