Loss of significance is an undesirable effect in calculations using floating-point arithmetic. It occurs when an operation on two numbers increases relative error substantially more than it increases absolute error, for example in subtracting two nearly equal numbers (known as catastrophic cancellation). The effect is that the number of accurate (significant) digits in the result is reduced unacceptably. Ways to avoid this effect are studied in numerical analysis.

The phenomenon can be demonstrated with decimal numbers.

The following example demonstrates loss of significance for a decimal floating point data type with 10 significant digits:

Consider the decimal number

A floating-point representation of this number on a machine that keeps 10 floating-point digits would be

which is fairly close — the difference is very small in comparison with either of the two numbers.

Now perform the calculation

The answer, accurate to 10 digits, is

However, on the 10-digit floating-point machine, the calculation yields

Tyler James Johnson (born June 7, 1981 in Columbia, Missouri) is a left-handed Major League Baseball relief pitcher who is currently in the Colorado Rockies Organization.

Johnson spent most of the 2006 season with the Cardinals' minor league team, the Triple-A Memphis Redbirds, but appeared in 56 games and pitched 36.1 innings with the St. Louis Cardinals. In the 2006 postseason, he pitched 7.1 innings and compiled a 1.23 ERA, including one scoreless inning pitched in the 2006 World Series, which the Cardinals won, defeating the Detroit Tigers, four games to one. He pitched again for the Cardinals in 2007 before becoming injured and missing the 2008 season. He was non-tendered following the 2008 season.

On February 5, 2009, Johnson signed a minor league contract with an invitation to spring training with the Seattle Mariners. After 2 months in the minors rehabbing, Johnson was released on June 6.

Signed a minor league contract for 2012 season with Colorado Rockies.

Bruce Hoffman is the Director of the Center for Security Studies at Georgetown University's Walsh School of Foreign Service and a specialist in the study of terrorism and counter-insurgency. He previously was Director of the RAND Corporation's Washington Office (1998-2006), Vice President for External Affairs at RAND (2001-2004) and held the RAND Corporate Chair in Counterterrorism and Counterinsurgency (2006-2006). Hoffman's publications include the books Inside Terrorism (1998; 2nd expanded and revised edition 2006); and, The Failure of Britain's Military Strategy in Palestine, 1939-1947 (1983). He is the editor-in-chief of the scholarly journal, Studies in Conflict and Terrorism; and, the series editor of Columbia Studies in Terrorism and Irregular Warfare, published by Columbia University Press. He holds a BA from Connecticut College and a B.Phil. and D.Phil. from University of Oxford.