rounding error

Rounding error is the difference between a rounded-off numerical value and the actual value. A rounded quantity is represented by a numeral with a fixed number of allowed digits, with the last digit set to the value that produces the smallest difference between the rounded quantity and the actual quantity.

Rounding can produce a value that is easier to deal with than the actual value, especially if the actual value contains a lot of digits. Rounding can also be done to indicate the relative precision of a value. For example, the irrational number pi equals approximately 3.14, rounded to two decimal places or three significant digits.

As an example of rounding error, consider the speed of light in a vacuum. The official value is 299,792,458 meters per second. In scientific (power-of-10) notation, that quantity is expressed as 2.99792458 x 10⁸. Rounding it to three decimal places yields 2.998 x 10⁸. The rounding error is the difference between the actual value and the rounded value, in this case (2.998 - 2.99792458) x 10⁸, which works out to 0.00007542 x 10⁸. Expressed in the correct scientific notation format, that value is 7.542 x 10³, which equals 7542 in plain decimal notation.