Dear Sally:

I have a page Operations on Fractions where I outline my view on common fractions (a/b) and operations on them. The division rule is related to in the bottom paragraph of the page.

Now, with regard to the decimal point, I would like to know what you think of the problem because I only can point to the known fact that the decimal notation is a shorthand for the expansion of a number in the decimal system. The decimal point simply indicates the position in a list of coefficients after which the powers of 10 become negative. And there also is a distributive law that tells you that instead of multiplying by 10 a sum of terms, one can multiply each term individually and then sum up the results.

So what would be your answer to the second of your questions?

Sincerely,
Alexander Bogomolny

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