How do you calculate #(7.8times10^7)/(1.0times10^4)#?

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Answer 1 · 2016-10-22T15:05:44

#7.8xx10^3#

In algebra we would simplify the following by dividing the numbers and subtracting the indices of like bases

#(color(red)(12)color(blue)( x^11))/(color(red)(4)color(blue)(x^5))" " rarr(cancel12^3 xx x^11)/(cancel4 xx x^5#

=# color(red)(3)color(blue)( xx x^6)" " (11-5=6)#

=#3x^6#

In scientific notation you do EXACTLY the same:
Divide the numbers and subtract the indices of like bases.

#(color(red)(7.8)color(blue)( xx 10^7))/(color(red)(1.0)color(blue)( xx 10^4)#

=#color(red)(7.8)color(blue)( xx 10^3)#

=#7.8xx10^3#