Problems from 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.

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Development:

$$a=783,623$$

$$b=126,961$$

$$a\cdot b:$$ 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 $$\dfrac{(a\cdot1000)}{(b\cdot1000)}$$ $$\dfrac{a}{b}=6,17$$

Solution:

$$a\cdot b=99489,56$$

$$\dfrac{a}{b}=6,17$$

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