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Welcome to our Math lesson on Applications of Significant Figures, this is the ninth lesson of our suite of math lessons covering the topic of Rounding and Significant Figures, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
Significant figures have a wide range of applications in practice. For example, if the perimeter P of an equilateral triangle is 8.00 cm and we want to calculate the side length L, we write
However, it is clear that we cannot express the result in this way, as we cannot be that precise in measurements. This means we have to express the result at only two decimal places as this is the tiniest division of units. Therefore, e must write the result at three significant figures: one before the decimal point and two after it. Hence, we must write the result as L = 2.67 cm.
The sides of a quadrilateral are 3.2 dm, 5 dm, 4.32 dm and 7.29 dm. Calculate the perimeter of this quadrilateral and express the result in the correct number of significant figures.
The perimeter of a quadrilateral is the sum of all sides. Hence, we have
However, it makes no sense to write the result like this, as one of the sides (the 5 cm one) is measured in whole decimetres, so we must write the result in decimetres as well to ensure it fits the least precise measurement. Therefore, we must round the result to the nearest whole number, i.e. P ≈ 20 dm. Hence, it is written in one significant figure, as the number taken as a reference to determine the precision of result (the number 5) has only one significant figure.
Apparently, the rounded result seems less accurate than the original. However, in science we prefer to be sure in the correctness of our findings. Therefore, it is better to round the result and give an approximate value to the correct result than to make groundless assumptions.
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