(1.00001)(0.99999) - (1.00002)(0.99998) = (100001/100000)*(99999/100000) - (100002/100000)*(99998/100000) =

Right here from the get go we see that the denominator of the expression above is 100000*100000 = 10^(-10) - Denominator, and we live it right there and focus on the numerator.

100001*99999 = (100000+1)*99999=100000*99999+99999

100002*99998 = (100000+2)*99998 = 100000*99998+2*99998

= 100000*99999+99999-100000*99998-2*99998 = 100000+99999-2*99998 = 100000+99999-2*(99999-1)=100000+99999-2*99999+2=100000-99999+2=3 - Numerator

Or, 3*(10^(-10) = 3/10^(10)

The numbers might look intimidating and cumbersome, but a little manipulation goes a long way. Or, once you got the denominator you can cross out some answer choices and guess in case you running out of time.

Please, feel free to correct me, if I went awry

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God loves the steadfast.