TITLE: What does "within $x$% of $y$" mean?
QUESTION [5 upvotes]: I cannot find a specific definition for "within $x$% of $y$". If I want a number within $10$% of $100$, am I looking for numbers in the set $[90,110]$? Or does it mean percentage difference? Or percentage change?

REPLY [2 votes]: If I want a value, let's call it $a$, that lies within $x$% of $y$,$^\dagger$ then I want
$$y\left(1-\frac{x}{100}\right) \le a \le y\left(1+\frac{x}{100}\right)$$
Following your (correct) example, if I want a value $a$ that lies within $10$% of $100$, then
$$90 \le a \le 110$$
In plain(er) English, if you see this statement in the context of a measurement, it means that our measurement's accuracy is bounded by some percentage of the desired value. This is to say we may have some uncertainty within the measurement. In another context, we might feel comfortable with such uncertainty. Then this range indicates our accepted tolerance compared to some ideal value.

$^\dagger$Note: I'm making the assumption that $y>0$. littleO posted a more complete answer.