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\frac{0.008}{0.99\times 0.2+0.01\times 0.8}
Multiply 0.01 and 0.8 to get 0.008.
\frac{0.008}{0.198+0.01\times 0.8}
Multiply 0.99 and 0.2 to get 0.198.
\frac{0.008}{0.198+0.008}
Multiply 0.01 and 0.8 to get 0.008.
\frac{0.008}{0.206}
Add 0.198 and 0.008 to get 0.206.
\frac{8}{206}
Expand \frac{0.008}{0.206} by multiplying both numerator and the denominator by 1000.
\frac{4}{103}
Reduce the fraction \frac{8}{206} to lowest terms by extracting and canceling out 2.