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The solution suggests to turn all the expressions into scientific notation and then simplify but I was wondering if anyone here had any mind boggling tricks to do this in a more elegant manner?

(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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The solution suggests to turn all the expressions into scientific notation and then simplify but I was wondering if anyone here had any mind boggling tricks to do this in a more elegant manner?

The solution suggests to turn all the expressions into scientific notation and then simplify but I was wondering if anyone here had any mind boggling tricks to do this in a more elegant manner?

The solution suggests to turn all the expressions into scientific notation and then simplify but I was wondering if anyone here had any mind boggling tricks to do this in a more elegant manner?

1.00001*0.99999 .... ends in 9, and 1.00002*0.99998 ends in 6 , thus answer has to be in the form 3*10^-x , option c or E

but since multiplication of each term around the subtraction operation will yield 10^-x < 10^-5 thus x > 5 .... thus option c