In the drawing above, the goal is to read a well-defined arrow. Depending on the situation, there may be other issues that affect the ease of reading. Real measuring instruments, such as graduated cylinders, have those issues. How meaningful is a drawing of a measurement scale, such as the one in the example above? It illustrates one particular issue very well: how to read a scale per se, figure out what the marks and labels mean, and how to estimate the final digit. 4.78 mL is 3 Significant Digits the last Significant Digits is not certain, but is "close". No one should say 4.72 mL! That is, the estimate is 4.78 mL to about +/- 0.01 mL. Some people might say 4.77 mL or 4.79 mL. This corresponds, of course, to writing one more digit "as best we can".) (It is a common rule of thumb to estimate the last digit to 1/10 the distance between the lines. We will estimate the position of the arrow to 1/10 the distance between the little lines, that is, to the nearest 0.01 mL.The arrow is clearly between 4.7 and 4.8 mL.The little lines (between the numbered lines) are 0.1 mL apart.Our goal is to read the scale at the position of the arrow. The arrow marks the position of a measurement. The specific scale is from a 10 mL graduated cylinder - shown horizontally here for convenience. The scale shown here is a "typical" measurement scale. A bad way to start with Significant Digits is to learn a list of rules. We will do that here, using drawings of measurement scales. An alternative is to use an activity that simulates taking measurements - of various accuracy. The best way to start with Significant Digits is in the lab, taking measurements. The number of high priority rules about Significant Digits is small. We will leave special cases for a while, so they do not confuse the big picture. This involves a few basic ideas, which can be stated as rules. Better - and what we will do here - is to emphasize the logic of using Significant Digits. If all the rules are presented together, it is easy to get lost in the rules. Unfortunately, there are "special cases" that can come up with Significant Digits. Almost everything about Significant Digits follows from how you make the measurements, and then from understanding how numbers work when you do calculations. Significant Digits is not a set of arbitrary rules. Using Significant Digits is one simple way to record the quality of the information.Ī simple and useful statement is that the significant figures (Significant Digits) are the digits that are certain in the measurement plus one uncertain digit. When you take a measurement, you record not only the value of the measurement, but also some information about its quality. If there is a discrepancy between any information here and your own course, please let me know - or check with your own instructor. There is no claim that one approach is "right" or even "better". Trying two approaches can be better than trying only one. Sometimes, looking at things differently can help. Think of it as another approach - to the same thing. If you were completely happy with how the Significant Digits topic is presented in your own course, you probably wouldn't be reading this page. However, what may be different is the order of presenting things, with a different perspective in the approach - the steps - to learning Significant Digits. The information here should agree, for the most part. One is about the information per se, and the other is about priorities, about the approach to thinking about Significant Digits. What if the advice given here disagrees with what your book or instructor says?
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