GNU BC: How is the “modulo” (%) with scale other than 0 useful?

This is a **self-answered** question, the research that is reasonable to ask for a question goes in the answer part, Please do not downvote because you believe I have not researched enough for an answer. Thanks. In any case, there is no description (that I can find) of this characteristic of bc in this site. When using bc, the % operator is claimed to calculate the "remainder", and yes, it works for integer numbers and when the **scale is zero**: $ bc <<<' scale=0; 27 % 7 ' 6 But it fails to give the "integer remainder" if the scale is not zero: $ bc <<<' scale=10; 27 % 7 ' .0000000003 Why (or how) is this definition of the % modulo useful?