10% lower and 10% higher of 100

Question

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 $110$?

Answer 1

Yes.

But maybe it is less confusing to say 10% lower/higher than 100, or 10% below/above 100.

Answer 2

I think you are right. $10\%$ higher of $100$ will be $110$ and lower will be $90\%$ .

Answer 3

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: $$100-\left(100\cdot \frac{10}{100}\right)=100-10=90$$