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Station  6We speak 1 ← 10 Machine

A $1\leftarrow 10$ machine has $1$, $10$, $100$, $1000$, and so on as dot values.

Here ten $1$s make $10$,
and ten $10$s make $100$,
and ten $100$s make $1000$,
and so on.

Question 1

Check again. Show that the code for $273$ is $273$.

Question 2

We speak the language of a $1\leftarrow 10$ machine!

When we write $273$ in words, we write

$273$ = two hundred seventy three

We literally say, in English at least, two HUNDREDS and seven TENS (that “ty” is short for ten) and three.

There are some cultures on this planet that have used base twenty. Why might they have chosen that number do you think?

In fact there are vestiges of base twenty thinking in western European culture of today. For example, in French, the number $87$ is spoken and written as "quatre-vingt-sept", which translates, word for word, as "four twenties seven." In the U.S. the famous Gettysburg address begins: "Four score and seven years ago." That’s four-twenties and seven years ago.

All right. The point of today’s lesson has been made. We have discovered base-ten place value for writing numbers and seen their context in the whole story of place value. We humans happen to like base-ten in particular because that is the number of fingers most of us seem to have.

In the next island we’ll start doing arithmetic with numbers, but in new and fabulous ways!

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