### Video Transcript

If the mass of object A is three
plus or minus 0.02 kilograms and the mass of object B is 800 plus or minus 30 grams,
then the total mass of the two objects equals blank. (A) 3.8 plus or minus 30.02
kilograms, (B) 830 plus or minus 0.05 kilograms, (C) 3.8 plus or minus 0.05
kilograms, (D) 830 plus or minus 30.02 kilograms.

We want to figure out which of
these four answer options correctly fills in the blank. In this question, we’re adding
together the masses of two objects, object A and object B. Let’s call the mass of object A 𝑚
sub A and the mass of object B 𝑚 sub B.

We can notice that these two masses
are expressed in different mass units, kilograms and grams. We also see that all four of our
answer options are given in units of kilograms. This tells us that before we
combine these masses, we’ll want to convert the mass of object B into units of
kilograms. Because one gram is equal to 10 to
the negative three or one one thousandth of a kilogram, we can write 𝑚 sub B as 800
plus or minus 30 all multiplied by 10 to the negative three kilograms. If we multiply through by 10 to the
negative three, we can see that the mass of object B can be expressed as 0.8 plus or
minus 0.03 kilograms.

It will now be more straightforward
to add together these two masses 𝑚 sub A and 𝑚 sub B. When we combine them, three plus
0.8 gives 3.8, and then 0.02 plus 0.03 is equal to 0.05. The total mass of these two objects
then expressed in units of kilograms is 3.8 plus or minus 0.05 kilograms. We note that this agrees with
answer choice (C).

Our completed sentence reads if the
mass of object A is three plus or minus 0.02 kilograms and the mass of object B is
800 plus or minus 30 grams, then the total mass of the two objects equals 3.8 plus
or minus 0.05 kilograms.