sigfigs rounding numbers basics

After my post the other day about rounding errors, I got a ton of requests to explain the idea of significant figures. That's actually a very interesting topic. The idea of significant figures is that when you're doing experimental work, you're taking measurements - and measurements always have a limited precision. The fact that your measurements - the inputs to any calculation or analysis that you do - have limited precision, means that the results of your calculations likewise have limited precision. Significant figures (or significant digits, or just "sigfigs" for short) are a method of…