The mass of a killer whale is 950,000,000 milligrams. What is its mass, in kilograms, expressed in scientific notation?

We can use conversion factors to get this answer. Let's begin by putting our number into scientific notation in the original units.

#950,000,000 mg = 9.5 xx 10^8 mg#

A conversion factor is a fraction that is equal to #1# such that multiplying anything by it will leave the actual quantity the same, but with different units. In our case we are trying to convert from #mg# to #kg#. We know how many #mg# are in a #g#

#1g = 1000mg implies (1g)/(1000mg) = 1 implies (1000mg)/(1g)=1#

we can also re-write these in scientific notation

#1g = 1xx10^3mg implies (1g)/(1xx10^3mg) = 1 implies (1xx10^3mg)/(1g)=1#

We can do the same for #kg# to #g#

#1kg = 1xx10^3g implies (1kg)/(1xx10^3g) = 1 implies (1xx10^3g)/(1kg)=1#

Now we just choose the fractions that have the units in the right location to cancel the units we don't want, leaving behind the units we do want:

#9.5 xx 10^8 color(red)(cancel(mg)) * (1 color(blue)(cancel(g)) )/(1xx10^3 color(red)(cancel(mg)) )*(1kg)/(1xx10^3 color(blue)(cancel(g) )#

then, multiplying powers leads us to add the exponents

#=(9.5 xx 10^8)/(1xx10^(3+3)) kg = (9.5 xx 10^8)/(1xx10^6) kg#

and and exponent in the demonimator is the same as the negative exponent in the numerator, i.e.

#=9.5 xx 10^8*1xx10^-6 kg = 9.5 xx 10^(8-6) kg#

finally

#950,000,000 mg = 9.5 xx 10^2kg#