Imagine you are in Science class. You recently received the results from your last test. You received a (insert grade here). However, you scored incorrectly on a problem because you rounded to the wrong decimal place. After politely arguing with your teaching in an attempt to forage for a couple of points, you concede defeat, and wish your teacher had explained the reason for rounding to a seemingly arbitrary number. Then you come to your senses. It’s not like you’ll ever use this stuff outside of science class, at least, not in the near future. Little did you know how wrong your conjecture was…..
Promptly afterward, you saunter to your english class. Relieved by the change of topic, you quickly compose a short essay on ancient warfare. Worn by your last altercation, you ignore the blatantly obvious fact that the topic was better suited to a world history class. Your late obsession with The Hunger Games left archery as the clear focus. After repeated comments on the accuracy of the ancient bowmen, you nonchalantly search the internet for a synonym for accuracy. After substituting various “accuracies” for “precisions”, your science teacher senses a disturbance in the scientific universe, materializes in your English class, and proceeds to give you a confusing rant on the difference between accuracy and precision. Then your science teacher remarks that there is a method to madness, and you realize that maybe, just maybe, there is order to the universe as we know it.
Despite the seeming irrelevance of the above paragraphs, I feel they emphasize the importance of these concepts in the scientific community. Let’s explain significant digits. No matter what measurement system you use, there will always be inaccuracy. It is an unavoidable part of scientific study. Scientists use significant figures to clarify these innate inaccuracies. The last digit in the number is always an estimate. For example, in the article we were supposed to read prior to the blog, the weight of gold was changed from 196.9~(4) to 196.9~(5) atomic mass units (amu). The last digit is one the scientists are estimating. This attention to detail is crucial to ensure the best results. If the weight of gold was rounded to 197 amu, it may have not affected some calculations, but in today’s world of advanced math and science, that small fraction is crucial.
Accurate and precision, despite their interchangeability in normal use, are different in a scientific context. Accuracy is how close the measurement is to the actual object, while precision is the repetition of the measurement. A common way to clarify this is to imagine accuracy as an array of bullet points fairly close to the center of a target. Precision is a close bunch of points, with no regard to the center of the target. This probably explains your science teacher’s passionate speech regarding the subject. As to how this applies to the article’s measurements, the change it digits would increase the measurements accuracy.
So, that is the big deal about significant digits, accuracy, and precision. They are a fundamental part of science that are necessary to ensure that scientific measurements are consistently reliable.