Station G
Multiplying by 10

We saw earlier that $26417 \times 10$ is $264170$ . The answer looks like the original number with a zero tacked on its end.

In fact, I remember being taught this rule in school: To multiply by ten, tack on a zero. For example,

$37\times 10 = 370$
$98989\times 10 = 989890$
$100000\times 10 = 1000000$

and so on.

This observation makes perfect sense in the dots-and-boxes thinking.

Let’s go!

Question 1

Here’s the number $26417$ in a $1\leftarrow 10$ machine. (Is it okay if I write numbers rather than draw dots?)

I3SG-image62

Here’s $26417 \times 10$ .

I3SG-image64

Now let’s perform the explosions, one at a time. (We’ll need an extra box to the left.)

Since $2$ groups of ten explode to give $2$ dots one place to the left, and $6$ groups of ten explode to give $6$ dots one place to the left, and $4$ groups of ten $4$ dots one place to the left, and so on, none of the digits we see ever change. In fact, the net effect we see is all digits “shifting” one place to the left and leaving zero dots in the ones place.