Multiplication and division of decimal numbers
Define two decimal numbers $a$ and $b$ of $3$ digits of integer part and $3$ digits of fractional part. Calculate its product and the $a/b$ division. Note: Use the following matrix to calculate the product:
| $a_5$ | $a_4$ | $a_3$ | $a_2$ | $a_1$ | $a_0$ | ||||||
| X | $b_5$ | $b_4$ | $b_3$ | $b_2$ | $b_1$ | $b_0$ | |||||
| $=$ | x | x | x | x | x | x | x | x | x | x | x |
where $a_0 \cdots a_5$, $b_0 \cdots b_5$ are the digits of $a$ and $b$, respectively, and $x$ the digits of the result.
$$a=783,623$$
$$b=126,961$$
$a\cdot b:$ The product is done without fractional digits and the comma is placed so that it has $3+3=6$ fractional digits.
| $7$ | $8$ | $3,$ | $6$ | $2$ | $3$ | ||||||
| X | $1$ | $2$ | $6,$ | $9$ | $6$ | $1$ | |||||
| $7$ | $8$ | $3$ | $6$ | $2$ | $3$ | ||||||
| $4$ | $7$ | $0$ | $1$ | $7$ | $3$ | $8$ | |||||
| $7$ | $0$ | $5$ | $2$ | $6$ | $0$ | $7$ | |||||
| $4$ | $7$ | $0$ | $1$ | $7$ | $3$ | $8$ | |||||
| $1$ | $5$ | $6$ | $7$ | $2$ | $4$ | $6$ | |||||
| $7$ | $8$ | $3$ | $6$ | $2$ | $3$ | ||||||
| $=$ | $9$ | $9$ | $4$ | $8$ | $9,$ | $5$ | $5$ | $9$ | $7$ | $0$ | $3$ |
$\dfrac{a}{b}$: since the number of decimal is the same in $a$ and $b$, the commas can be ignored, and now compute the division of the integers $\dfrac{(a\cdot1000)}{(b\cdot1000)}$ $\dfrac{a}{b}=6,17$
$$a\cdot b=99489,56$$
$$\dfrac{a}{b}=6,17$$