Guard Digits vs. Roundoff Error vs. Overall Uncertainty
John Denker, Larry Smith · The Physics Teacher · 2018
Roundoff error is an error. It can be dramatically reduced by the use of additional low-order digits, i.e. guard digits. Although the significant-figures idea in its standard form is incompatible with guard digits, this problem can be neatly solved by underlining the last “significant” digit, and then appending guard digits to the right of there. This clarifies the distinction between roundoff error and overall uncertainty while preserving compatibility with sig figs. The focus here is on reducing roundoff error; we defer discussion of most other contributions to the uncertainty.