SOLUTION: Convert 12kg/ml into grams/liter

Question 94772: Convert 12kg/ml into grams/liter
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given:
.

.
To convert this to we need to recall that:
.
1 kg = 1000 gms
and
1 ltr = 1000 mls
.
We are going to multiply the original amount we were give by two conversions, one conversion
that changes kg to gms and one that changes ml to ltrs. So we have to have our conversions
arranged so that the kg in the conversion will cancel the kg in the problem we were given
and the ml in the conversion will also cancel the ml in the problem we were given.
.
To cancel the kg in the given problem (which is in the numerator) we need a kg in the
denominator. So our conversion factor will have kg in the denominator and gms in the numerator.
So the weight conversion must be:
.

.
To cancel the ml in the given problem (which is in the denominator) we need a ml in the numerator.
So our conversion factor will have ml in the numerator and ltr in the denominator.
That means that this conversion factor for the liquid measure must be:
.

.
Now all that we need to do is to multiply the original given by these two conversion
factors as follows:
.

.
Notice how the weight units cancel:
.

.
Next notice how the liquid measure units also cancel:
.

.
Then notice that in the denominators we can ignore the "1" associated with the kg and with
the ltr.
As a result we are left with:
.

.
You can now see that the remaining units are gms in the numerator and ltr in the denominator,
just as the problem asked for. All you have to do is multiply the numbers that all appear
in the numerator
to get:
.

.
To shorten this you can write the answer in the form of exponential notation as:
.

.
or in scientific notation as:
.

.
Once you get the hang of this process, it will go much faster for you. In each of the conversion
factors you relate the equivalent amounts: 1 kg and 1000 gms, 1 ltr and 1000 ml, or any
other equivalent amounts that you may need ... 1 ton and 2000 lbs, 1 gallon and 4 quarts,
and so on. Then all you have to do is decide which part of the equivalence goes into the
numerator of your conversion factor and which goes into the denominator of the conversion factor.
That decision depends on how you need to place them to cancel the units in the given
problem. The more of these types of problems you do, the more logical the process
will become to you. And you will become aware that you may need to have more conversion
factors in the multiplication chain to work your way to the units you need in the solution.
.
Hope this helps you to work your way through this problem and others like them.
.

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