What is #(1.00 xx 10^48 m^5) / ((2.00 xx10^28 m) (2.50 xx 10^25 m))# ?

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Answer 1 · 2017-05-29T11:23:41

The question is in engineering terms so the answer must be the same form.

#2.0xx10^(-6)m^3#

#color(blue)("Dealing with "m)#

#m^5/(mxxm)" "=" "m^5/m^2" "=" "m^3xxm^2/m^2" "=" "m^3#

Different approach:

#m^5/(mxxm)" "=" "m^5/m^2" "=" "m^(5-2)" "=" "m^3 #
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Dealing with the 10's")#

#10^(48)/(10^(28)xx10^(25))" "=10^(48)/(10^(28+25))" "=" "10^(48)/(10^(53))#

#=" "10^(48-53)" "=" "10^(-5)#

Note that this is the same as #1/(10^5)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Dealing with the numbers")#

#1/(2xx2.5) = 1/5#

#color(green)(1/5color(red)(xx1)" "=" "1/5color(red)(xx2/2)" "=" "2/10=0.2#

But this is the same as #2xx1/10#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Putting it all together")#

#2xx1/10xx1/10^5xxm^3#

This is the same as:

#2.0xx10^(-6)m^3#