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 tracking measurement precision, in a way that allows you to propagate your precision limits throughout your calculation.
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