# Precision (arithmetic)

The precision of a measurement or value describes the number of digits that are used to express that value. This might be the total number of digits (sometimes called the significant digits) or, less commonly, the number of fractional digits or places (the number of digits following the point).

In both cases, the term precision can be used to describe the position at which an inexact result will be rounded. For example, in floating-point arithmetic, a result is rounded to a given or fixed precision, which is the length of the resulting significand. In financial calculations, a number is often rounded to a given number of places (for example, to two places after the point for many world currencies).

As an illustration, the decimal quantity 12.345 can be expressed with various numbers of significant digits or decimal places. If insufficient precision is available then the number is rounded in some manner to fit the available precision. The following table shows the results for various total precisions and decimal places (rounding is towards zero).

Precision
Rounded to
significant digits
Rounded to
decimal places
Five 12.345 12.34500
Four 12.34 12.3450
Three 12.3 12.345
Two 12 12.34
One 1E+1 12.3
Zero n/a 12
<p> The notation 1E+1 means: 1 × 10+1.

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