Video Transcript
If one decimeter is equal to 10
centimeters, which of the following is one decimeter cubed equal to? (A) 10 centimeters cubed, (B) 1,000
centimeters cubed, (C) 1,000 centimeters, (D) 100 centimeters cubed, (E) one
centimeter cubed.
In order to solve this problem, we
will need to use dimensional analysis. Dimensional analysis is a
problem-solving method for converting between two different units. In this method, the original value
is multiplied by a conversion factor or several conversion factors if necessary. A conversion factor is a
relationship of two equal quantities that have different units. The question provides us with a
conversion factor: one decimeter is equal to 10 centimeters.
To perform dimensional analysis,
this conversion factor will need to be written as a fraction. We can write this conversion factor
as two different fractions, one decimeter per 10 centimeters or 10 centimeters per
one decimeter. The fraction that we will choose to
solve the problem depends on the original value. The original value, the value that
we are trying to convert, is one decimeter cubed. We need to multiply our original
value by a conversion factor or factors such that the unit decimeters cubed will
cancel. When multiplying or dividing, units
will cancel when they appear in both the numerator and denominator.
In the original value, the unit
decimeter cubed appears in the numerator. This means that we should choose
the conversion factor where the unit decimeters appears in the denominator. We can then proceed to multiply by
the correct conversion factor. However, multiplying by the
conversion factor only one time will not allow the unit decimeters cubed to be
completely canceled.
A decimeter cubed is a volume unit
that can be expanded to one decimeter times one decimeter times one decimeter. Here we can see that our unit
decimeters in the denominator can only cancel one instance of the unit decimeters in
the numerator. This means that we will need to
multiply by the conversion factor two more times so that all three instances of the
unit decimeter in the numerator will be canceled.
We can then perform the
calculation. This gives us the answer 1,000
centimeters times centimeters times centimeters. A unit that is multiplied by itself
can be written as a single unit with a power. The power indicates the number of
times the unit is multiplied by itself. The unit centimeters appears three
times. Thus, the unit can be rewritten as
centimeters cubed. By performing dimensional analysis,
we have determined that one decimeter cubed is equal to answer choice (B), 1,000
centimeters cubed.
