TITLE: 10% lower and 10% higher of 100
QUESTION [5 upvotes]: I'm confused about how to get the $10\%$ higher and $10\%$ lower of $100$. I'm alone I don't know if my idea is correct.  My idea is $10\%$ higher of $100$ is $110$, then the $10\%$ lower of $100$ is $90$, then the range $10\%$ higher and $10\%$ lower of $100$ is between $90$ to $110$?

REPLY [2 votes]: I think it is correct, in this case $100$ is exactly the $100\%$ of the quantity, so if you want a $10\%$ "higher" (or a $10\%$ over $100\%$), you want then $100\%+10\%=110\%$ of the quantity, which is in this case: $$100+\left(100\cdot \frac{10}{100}\right)=100+10=110$$
Likewise, if you want a 10% "lower" (or a $10\%$ under $100\%$), you want then the $100\%-10\%=90\%$ of the quantity, which is in this case: $$100-\left(100\cdot \frac{10}{100}\right)=100-10=90$$