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Accuracy - Rounding

significant penny tax digits

If you buy several items, all of which are subject to a sales tax, then you can calculate the total tax by summing the tax on each item. However, for the total tax to be accurate to the penny, you must do all the calculations to an accuracy of tenths of a penny (in other words, to three significant digits), then round the sum to the nearest penny (two significant digits). If you calculated only to the penny, then each measurement might be off by as much as half a penny ($0.005) and the total possible error would be this amount multiplied by the number of items bought. If you bought three items, then the error could be as large as 1.5 cents; if you bought 10 items then your total tax could be off by as much as five cents.

As another example, if you want to know the value of pi to an accuracy of two decimal places, then you could express it as 3.14. This could also be expressed as 3.14 +/- 0.005 since any number from 3.135 to 3.145 could be expressed the same way—to two significant decimal points. Any calculations using a number accurate to two decimal places are only accurate to one decimal place. In a similar example, the accuracy of a table can either refer to the number of significant digits of the numbers in a table or the number of significant digits in computations made from the table.

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