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

Question

Roman Alvarez · Accepted Answer

There are #2.45xx10^9# micrograms in #2.45xx10^3# grams .

#1# microgram is one-millionth of standard unit, which is gram here, Hence, one gram has #1,000,000# or #10^6# micrograms. and #2.45xx10^3# grams are equivalent to #2.45xx10^3xx10^6=2.45xx10^9# micrograms.

Noah Archer · Answer

#"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)#

#color(white)(.)#

#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))#

#color(white)(.)#

#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#

Gabriel Agustin · Answer

undefined To convert grams to micrograms, you multiply the number of grams by $10^6$, because there are $10^6$ micrograms in one gram.

Therefore, to find how many micrograms are there in $2.45 \times 10^3$ grams:

$$2.45 \times 10^3 \text{ grams} \times 10^6 = 2.45 \times 10^9 \text{ micrograms}$$

So, there are $2.45 \times 10^9$ micrograms in $2.45 \times 10^3$ grams.