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Arithmos
Arithmos
Arithmos

Station  G
Multiplying by 10 

We saw earlier that 26417×1026417 \times 10 is 264170264170. 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,

37×10=37037\times 10 = 370
98989×10=98989098989\times 10 = 989890
100000×10=1000000100000\times 10 = 1000000

and so on.

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

Question 1

Here’s the number 2641726417 in a 1101\leftarrow 10 machine. (Is it okay if I write numbers rather than draw dots?)

I3SG-image62

Here’s 26417×1026417 \times 10.

I3SG-image64

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

Since 22 groups of ten explode to give 22 dots one place to the left, and 66 groups of ten explode to give 66 dots one place to the left, and 44 groups of ten 44 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.

I3SG-image71

Indeed it looks like we just tacked on a zero to the right end of 2641726417. (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 476×10476\times 10?
To 476×100476\times 100?

Question 3

What must be the answer to 9190÷109190\div 10?

Question 4

What must be the answer to 3310000÷1003310000\div 100?

You can either play with some of the optional stations below or go to the next island!

Arithmos
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