## 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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