How many micrograms are there in ##2.45*10^3## grams?

##"micrograms "=2.45xx10^3xx10^6" "=" "2.45xx10^9##

##color(blue)("Establishing the ratio format and content")##

1 microgram ##= 1xx10^(-6)" grams " larr " 1 millionth of 1 gram"## ##color(white)(.)##

##color(red)("Using ratio")##

##("micrograms")/("grams") ->color(magenta)(1/(10^(-6))) -=("micrograms")/(2.45xx10^3)##

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##color(red)("but "1/10^(-6) " is the same as "(10^6)/1)##

##color(white)(.)##

##("micrograms")/("grams") ->color(magenta)((10^6)/1) -= ("micrograms")/(2.45xx10^3)##

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ##color(blue)("The calculation")##

##color(brown)((10^6)/1 -=("micrograms")/(2.45xx10^3))##

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##color(red)("Multiply bot sides by "color(blue)(2.45xx10^3))##

##color(white)(.)##

##color(brown)((10^6)/1 color(blue)(xx2.45xx10^3) " "=" micrograms "xx(color(blue)(cancel(2.45xx10^3)))/(cancel(2.45xx10^3)) )##

##color(white)(.)##

##"micrograms "=2.45xx10^3xx10^6" "=" "2.45xx10^9##