Definition:Abridged Multiplication

Definition
Abridged multiplication is multiplication using only so many significant figures as are required to obtain a product with sufficient precision.

Let $x$, $y$ and $z$ be real numbers such that $x y = z$.

Let $n \in \Z$ be an integer.

Let $z$ be required to be rounded to the nearest $n$th power of $10$.

Let $x$ and $y$ be reported to the nearest $n - r$th and $n - s$th power of $10$ respectively.

Then to obtain a product which is accurate to the nearest $n$th power of $10$, it is necessary to perform the multiplication using $x$ and $y$ be reported to the nearest $n - 1$th power of $10$ only, and the less significant figures in $x$ and $y$ can be ignored.