Nocedal and Wright in their book Numerical Optimization have this:
... The four constants differ greatly in magnitude, since the reacions take place at vastly different speeds. Suppose we have the following rough estimates for the final values of the constants, each correct to within, say, an order of magnitude: $$x_1\approx 10^{-10}, x_2\approx x_1 \approx 1, x_4 \approx 10^5.$$...
in the same book:
...the optimal values of $z$ will be within about an order of magnitude of 1,...
What does it mean to be correct to within an order of magnitude? Two orders of magnitude? What does it mean to be within about an order of magnitude of a number?
"An order of magnitude" means "A factor of $10$". So, for instance, if we say that $x_1 \approx 10^{-10}$ is correct within an order of magnitude, that means that $x_1$ is definitely somewhere between $10^{-11}$ and $10^{-9}$. Two orders of magnitude similarily means two factors of $10$, or in other words, a factor of $100 = 10^2$.