Abridged Multiplication/Examples/Arbitrary Example

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Example of Abridged Multiplication

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 $x y$.


Demonstration

Performing the full multiplication:

    5.6982
 x      23
----------
   17.0946
  113.9640
----------
  131.0586
----------

which rounds to $131.06$.


Ignoring the $4$th decimal place:

    5.6982
 x      23
----------
   17.0946
  113.9640
----------
   17.094        -- dropping the 4th decimal place
  113.964
----------
  131.058
---------

which again rounds to $131.06$.

$\blacksquare$

Sources