algebra precalculus - Intuition behind multiplication

I recently read this post and the highest voted comment and it got me thinking. How does think about multiplication if it is decimals?

For example, if we have $3.9876542 \times 2.3156479$ then how would we multiply that? It doesn't make a lot of sense to add $3.9876542$, $2.3156479$ times. Then how would you think about multiplying that i.e. what's the intuition of behind that?

Thanks!

Answer

A rectangle with sides $3.9876542\,\mathrm m$ and $2.3156479\,\mathrm m$ can be viewed as $3987654200$ by $2315647900$ namometers instead. Then you can actually count all thos tiny square-nanometers (or simplify this by repaeted addition!) and obtain an area of $9234003074156180000\,\mathrm{nm}^2$. Since there are $1000000000000000000\,\mathrm{nm}^2$ in each $\mathrm m^2$, you end up with $9.23400307415618\,\mathrm m^2$ and thus we should have $3.9876542\cdot 2.3156479 = 9.23400307415618$.