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# Station  GMultiplying 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.

### Question 1

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

Here’s $26417 \times 10$.

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.

Indeed it looks like we just tacked on a zero to the right end of $26417$. (But this is really because of a whole lot of explosions.)

### Question 2

Some questions to ponder, if you like.

What must be the answer to $476\times 10$?
To $476\times 100$?

### Question 3

What must be the answer to $9190\div 10$?

### Question 4

What must be the answer to $3310000\div 100$?

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