it only works for ² and ³ though
and those problems are solved when you split the numbers and the powers of ten, like this, and remembering that you can only add numbers together when they multiply 10 to the same power:
(46.15 + 183.035)(7.14*10^-7)/(8.12*10^-3 + 7.77*10^5)=
(46.15*7.14*10^-7 + 183.035*7.14*10^-7)/(8.12*10^-3*
10^8*10^-8 + 7.77*10^5)
the red thing is actually 1, so i can multiply stuff by it and it won't change a thing
so
(46.15*7.14*10^-7 + 183.035*7.14*10^-7)/(
(8.12*10^-8)*10^5 + 7.77*10^5)
=
(46.15*7.14*10^-7 + 183.035*7.14*10^-7)/(
(0.0000000812)*10^5 + 7.77*10^5)
=
(46.15*7.14*10^-7 + 183.035*7.14*10^-7)/(
(7.7700000812)*10^5)
now the top part....it already has equal powers so I just have to calculate the expression's value.
(46.15*7.14*10^-7 + 183.035*7.14*10^-7)/(7.7700000812*10^5)
=
(
329.511*10^-7 +
1306.8699*10^-7)/(7.7700000812*10^5)
=
1636.3809*10^-7/(7.7700000812*10^5)
Now just divide the powers of 10 and the numbers.
1636.3809*10^-7/(
7.7700000812*10^5)
=
210.60243023154217055325299241646*10^-7*10^-5
=
210.60243023154217055325299241646*10^-12
=
2.1060243023154217055325299241646*10^-10
=~2.11*10^-10
Piece of piss
And actually, when you sum up two numbers with very different greatness orders (like 10^5 and 10^-3) you may consider the smallest one as zero.
Happy wanking.