How to solve #2.9 xx 10^(11) - 3.7 xx 10^(13)# ?

Given: #2.9 xx 10^11 - 3.7 xx 10^13#

In order to subtract, you want the exponents to be the same. This allows the decimals to line up for subtracting.

#2.9 xx 10^11 = 0.029 xx 10^13#

Now subtract the two numbers before the exponents:

#.029 - 3.7 = -3.671#

Since both numbers have the same exponents, the solution will have the same exponent:

#.029 xx 10^13 - 3.7 xx 10^13 = -3.671 xx 10^13#

Factor out #10^(11)# giving:

#10^(11)(2.9-3.7xx10^2)#

#10^(11)(2.9-370)#

If the subtraction of a greater value is giving you a problem do this:

make the -370 look as though it is +370 when really it isn't

Note that by example:

#2-4color(white)("dd")=color(white)("dd")1xx(2-4)color(white)("dd") =color(white)("dd")-1xx(-2+4)#

Applying the above approach we have:

#10^(11)(2.9-370)color(white)("d")=color(white)("d") -10^(11)(-2.9+370)#

Consider just the #-2.9+370# bit first:

#370.0#
#ul(color(white)(37)2.9 larr" Subtract")#

#3cancel(7)^6 cancel(0)^(10).0#
#ul(color(white)(37dd)2color(white)("dd").9 larr" Subtract")#

Still will not work so write:

#3cancel(7)^6 cancel(0)^(9).cancel(0)^10#
#ul(color(white)(37dd)2color(white)("d").color(white)(".")9 larr" Subtract")#
#3color(white)(".")6color(white)("d")7color(white)("d").color(white)("d")1#

So the answer to this part is #367.1#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Putting it all back together

# -10^(11)(-2.9+370) color(white)("d")=color(white)("d")-10^(11)(367.1) =-367.1xx10^(11)#

#color(white)("dddddddddddddddddddddddddddddd.d")=-3.671xx10^13#