Periods of repeating decimals!

A=0.19+0.199,B=0.19×0.199{A = 0.\overline{19} + 0.\overline{199}, \quad B = 0.\overline{19} \times 0.\overline{199}}

Recall that 0.19,0.\overline{19}, for example, stands for the repeating decimal 0.19191919...0.19191919... and that the period of a repeating decimal is the number of digits in the repeating part. In this case, the period of 0.190.\overline{19} is 2.

Find the sum of the periods of AA and BB.

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