digits = posint

A positive integer; the environment variable Digits will be set to this integer during the execution of this procedure. By default this is set to 10.

The NumberOfSignificantDigits command computes the number of significant digits of an approximation using the exact value and approximate value.

The number, SD, of significant digits is computed by the formula

This formula returns the largest integer $n$ such that $\mathrm{xe}$ and $\mathrm{xa}$ differ by less than $0.5$ units in the $n$th place.  For example, for $\mathrm{xe}=19.123456$ and $\mathrm{xa}=19.123955$ we have $n=5$, because the difference between $\mathrm{xe}$ and $\mathrm{xa}$ is $0.499$ units in the 5th place (digit), while for $\mathrm{xa}=19.123956$ we have $n=4$ because the difference is now $0.500$ units in the 5th place (so too large to set $n=5$).

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{NumericalAnalysis}\right]\right)\:$

$\mathrm{xe}≔1.81$

$\mathrm{xe}≔1.81$

$\mathrm{xa}≔1.63$

$\mathrm{xa}≔1.63$

$\mathrm{NumberOfSignificantDigits}\left(\mathrm{xe}\,\mathrm{xa}\right)$

$1$

$\mathrm{xe}≔9.81$

$\mathrm{xe}≔9.81$

$\mathrm{xa}≔9.63$

$\mathrm{xa}≔9.63$

$\mathrm{NumberOfSignificantDigits}\left(\mathrm{xe}\,\mathrm{xa}\right)$

$1$