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Approximation of Numbers


Numbers produced by a calculator are often inexact, because the calculator can work only with a finite number of decimal places. For instance, a -digit calculator gives  and, both of which are approximations of the true values.
Don’t be too quick to pick up your calculator –answers such as , ,  and are often preferred to much lengthy decimal expressions that are only approximations.

Most numbers obtained from measurements of real-world quantities are subject to error and also have to be regarded as approximations. If the result of a measurement (or any calculation involving approximations) is expressed in scientific notation, , it is usually understood that  should contain only significant digits, that is, digits that, expect possibly for the last, are known to be correct or reliable. (The last digit may be off by one unit because the number was rounded off). For instance, if we read in a physics that
                                      One Electron volt  joule
We understand that the digit ,  and are significant and we say that, to an accuracy of three significant digits, one electron volt is  joule.
            To emphasize that a numerical value is only an approximation, we often use a wave-shaped equal sign . For instance,
However, we sometimes are ordinary equal signs when dealing with inexact quantities, simply because it becomes tiresome to indicate repeated that approximations are involved.



(Concept of Rounding Off)


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