Imagine that you are a scientist with a measurement or calculation to your credit that has taken years of meticulous work. When your results are published, you find that your techniques are praised for their precision and your results are criticized for their lack of accuracy. How is this possible? We usually think of accuracy and precision as pretty much the same thing. But in science, these words are used in significantly different ways. A result is considered accurate if it is consistent with the true or accepted value for that result. The precision of a result, on the other hand, is an indication of how sharply it is defined. For example, the first few decimal places of the true value for the mathematical constant are 3.142, and the accepted value for the speed of light in a vacuum is 2.99792458 x 108 meters per second. Thus, 3.14 is an accurate value for to three digits precision, and 3.0 x 108 meters per second is an accurate value for the speed of light in a vacuum to two digits precision.
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Consider the calculation of by William Shanks. In 1853 he published a calculation of to 607 decimal places. Twenty years later, he published a result that extended this work to 707 decimal places. This was the most precise numerical definition of of its time and adorned many classroom walls. In 1949 a computer was used to calculate p, and it was discovered that William Shanks’s result was in error starting at a point near the 500th decimal place all the way to the 707th decimal place. Nowadays, with the benefit of a true value for to 100,000 decimal places, we can say that William Shanks’s techniques generated a precise result, but the value he obtained was not accurate.
are 3.142, and the accepted value for the speed of light in a vacuum is 2.99792458 x 108 meters per second. Thus, 3.14 is an accurate value for 
