Definition:Abridged Multiplication

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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.


Examples

Arbitrary Example

Let:

\(\ds x\) \(=\) \(\ds 5.6982\)
\(\ds y\) \(=\) \(\ds 23\)

Let it be required that $z = x y$ is to be rounded to $2$ decimal places.

Then, when we calculate:

$z = 5.6982 \times 23$

we can ignore the $4$th decimal place in the partial products of $x y$.


Also see

  • Results about abridged multiplication can be found here.


Sources

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