## 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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