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## Multiplication of Decimal Numbers

Since decimal numbers are implicitly just polynomials in the powers of 10, e.g.,

it follows thatmultiplying two numbers convolves their digits. The only twist is that, unlike normal polynomial multiplication, we havecarries. That is, when a convolution result exceeds 10, we subtract 10 from the result and add 1 to the digit in the next higher place.