Using significant figures in calculations in chemistry requires some knowledge of rules. Rules are based on the number of significant digits you would report after solving a problem requiring some type of calculation. The two rules are as follows, per Ebbing and Gammon:
- For calculations involving multiplication and division: The number of significant digits you would report in the answer to the calculation is the same as the number or measurement in the calculation with
*the least number of significant digits.* - For calculations involving addition and subtraction: The number of significant digits you would report in the answer to the calculation is based on the number of decimal places in the the measurement with
*the least number of decimal places*; report your answers to only this number of decimal places – not more!
As an oversimplified example, say you have the following calculation to perform (for now, we will leave out the intricate details including any units): 3.035 x 9.01234. Plugging this in to your calculator, you get 27.3524519. However, due to uncertainty in measurement of the two original values, this cannot be the final answer. You must use the rule above for calculations involving multiplication, in order to give the correct final answer. Since 3.035 is the number in the calculation with the least number of significant digits, which is four significant digits, the answer can correctly be reported as 27.35. Another oversimplified example, this time with addition, is as follows: 3.5234 + 2.3 is 5.8234. Hypothetically, however, these numbers are supposed to be measurements (despite the lack of units here), which means that you must find the number in the calculation with the least number of decimal places, which is 2.3, with only one decimal place. Therefore, the answer can be reported only as 5.8. This review was pretty short, but be aware that there are a few more things to review when solving quantitative problems in chemistry; namely, exact numbers and rounding are two other topics that must be reviewed before I can move on. I have been thinking of implementing a review sheet once I complete the review of the first chapter, which will be soon (yay!). The review sheet will consist of a short review of the entire chapter with typed notes, writing, and/or drawing, to sum things up and to help you focus on the key points that you should have taken away from the posts. The posts do often get lengthy so the review/summary will be a good way to keep on top of things.
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