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| The Reason for Significant Digits
| Trump’s Executive Effects
| If you divide 11.9 by 13.0, a calculator will offer an answer of 0.91538461538.... but you can round the number off to make it more manageable. In math, there is no rule specifying just where to round it off. However, in science and engineering, the rules of significant digits would round the answer to 0.915. Similarly, pi is a number that continues unendingly: 3.14159265.... A value is selected that matches the number of significant digits required for the problem. For three significant digits, pi is 3.14. If five are required, it is 3.1416.
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| In addition or subtraction, the answer should be rounded to match the least exact number. 12 + 270 + 8.23 = 290.23, but the correct answer is actually 290 since it should be expressed to the tens place. In multiplication or division, the answer should be rounded to match the fewest number of significant digits. 17 x 203 x 615 = 2,122,365, but the correct answer is actually 2,100,000 or 2.1 x 106.
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| To understand the use of significant digits in science and engineering, one must first understand the difference between accuracy and precision. I found that most students, and actually most individuals, feel that these terms are equivalent, but such is not the case. Accuracy measures how close an answer is to the true or correct value. Precision is a measure of how repeatable the answers are. The goal is to achieve both, but such may not always be the case.
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| For example, suppose that you step on a bathroom scale and it gives you a response of 312 pounds. Startled, you step off and reweight yourself. Once again it says that your weight is 312 pounds. You step off and check that it reads zero when nothing is on it. Again, it says that you weight 312 pounds. You shake the scale and try one more time. It still says that your weight is 312 pounds. The error is in the scale. While the answer given is precise, it is not accurate. There is something wrong with the equipment being used. I taught my classes to take equipment accuracy into account while striving for precision.
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| If you were told to cut out a card that is 5 cm by 12 cm, the odds are that you can do this fairly easily. As long as the width is at least 4.5 cm but less than 5.5 cm and the length is at least 11.5 cm but less than 12.5 cm, your result is accurate. What if you were instructed to cut a card that is 5.0 cm by 12.0 cm. Mathematically, the instructions appear to be the same, but the significant digits now play a critical role. To be accurate, the width must be at least 4.95 cm but less than 5.05 cm and the length must be at least 11.95 cm but less than 12.05 cm. This is far more difficult to do successfully!
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| On a lighter side, consider the following classic joke:
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| A woman visits the Sphinx and, asked by the guide if she knows its age, jokingly says, "Of course, it's about 4,500 years old... give or take a few decades." She then winks and adds, "A lady never reveals her age... or the true age of a monument she's fond of!"
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