Exploding Dots

1.4 The \(1 \leftarrow 10\) Machine

Lesson materials located below the video overview.

Okay. Let’s now go wild.

Let’s go all the way up to a \(1 \leftarrow 10\)  machine and put  \(273\) dots in a \(1 \leftarrow 10\) machine!

What is the secret \(1 \leftarrow 10\) code for the number \(273\)?

I thought my way through this by asking a series of questions.

Will there be any explosions? Are there any groups of ten that will explode? Certainly!

How many explosions will there be initially? Twenty-seven.

Any dots left behind? Yes. Three.

Okay. So there are twenty-seven explosions, each making one dot one place to the left, leaving three dots behind.

Any more explosions? Yes. Two more.

Any dots left behind? Seven left behind.


The \(1 \leftarrow 10\) code for two hundred seventy three is… \(273\). Whoa!


12. a) What is the\(1 \leftarrow 10\)  code for the number thirteen?

       b) What is the \(1 \leftarrow 10\) code for the number thirty-seven?

       c) What is the \(1 \leftarrow 10\) code for the number \(5846\)?


Something curious is going on!

What is the natural big question to ask?

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