Quick…one sentence…

What is the meaning of the decimal point?

Here is an illustration of the most common answer in my class (a math content course for prospective elementary and special ed teachers):

It’s not wrong, but it’s incomplete.

Thinking of the decimal point as the border between whole numbers and decimals limits our ability to think about relationships between these two domains.

In particular, look at that picture again. The essence of whole-number place value is right-to-left; the essence of fraction (decimal) place value is left-to-right if we’re thinking about the decimal point as the border.

But the same relationships hold on either side: If we move one place to the left, the value is 10 times greater and if we move one space to the right, the value is 1/10 as great.

No, the decimal point isn’t really the border between two different settlements.

And it’s not a the marker of symmetry either. Thinking about the decimal point this way leads us to expect that there should be a *oneths* place to the right of the decimal point.

No, the decimal point marks the most important location in a place value system: the ones place. Once we know where the ones place is, we know the value of every other place.

It is just an unfortunate accident of history that the decimal point lies to the right of the ones place, when really it should sit underneath it.