Hello, I´m a bit math-challenged and just started to brush up on both physics and mathematics simultaneously but I'm still at absolute beginner status and I don't want to go on in the book as long as I can't even figure out such a simple example. I'm using the Giancoli textbook on physics for self-study but can't quite follow the simplest of examples in the first chapter. Since the problem lies in the mathematical part of my understanding and not the conceptually physical part I thought I'd post it here. Just wanted to check if I'm doing something wrong or whether there's a typo in the example because unfortunately there doesn't seem to be a list of errata for the book. Here it is: 1. The problem statement, all variables and given/known data The example is about estimating the volume of a lake by using some rough measures and rounded-off numbers to get at the approximate order-of-magnitude. So it says: V=hπr2 ≈(10meters) × (3) ×(5×102meters)2≈8×106m3 ≈ 107 m3 where π has been rounded to 3, the average depth of the lake is 10m and the estimated radius of the surface is given by 5×102 (500 m). I can't seem to follow how he arrives at 8 ×106. 2. Relevant equations - 3. The attempt at a solution In my mind it would come to 3×(5×105) and then maybe 1.5×101 ×105 and then 1.5 ×106. This is of course different from the given 8×106. I figure I'm probably making a mistake here in the rules of multiplication of exponents and bracketing out but I can't figure out what it is. Any help would be much appreciated. Sorry for the absolute rookie level of mathematical (in)competence.