Video Transcript
Which of the following values has the greatest length? (A) One million micrometers, (B) one meter, (C) 1000 centimeters, (D) 100
centimeters, (E) 100000 millimeters.
This question is asking us to pick the answer choice with the greatest length. However, the answer choices are presented in a variety of units. In order to compare these values with different units, we need to know how the units
compare to one another.
For example, the prefix kilo- represents a multiplication factor of 1000. So a kilometer is 1000 times longer than the base unit of a meter, and a kilogram is
1000 times heavier than the base unit of a gram. Similarly, a centimeter, symbolized as cm, is one one hundredth the length of a
meter. In other words, it’s 100 times smaller. A millimeter is 1000 times smaller than the base unit of a meter. And a micrometer, symbolized by the lowercase Greek letter 𝜇 before the m, is the
unit one million times smaller than a meter.
We want to convert these various units into the same unit in order to compare
them. To do that, we need to use conversion factors. For example, to convert one million micrometers into meters, we use the conversion
factor of one meter over one million micrometers. One important feature of a conversion factor is that it has equivalent values in the
numerator and denominator. In this case, one meter is equivalent to one million micrometers, so the conversion
factor is equivalent to one.
Since we are essentially multiplying by one, we can use conversion factors to change
the units of the measurement without changing the quantity or amount of the
measurement. Our answer in meters, one meter, is equivalent to the initial measurement of one
million micrometers.
For problems like this, we want to ensure that we write our conversion factor with
the starting unit in the denominator and the ending unit in the numerator. That way, the starting unit is canceled out by the denominator. Doing it the other way around does not cancel out the units and gives us an answer
that doesn’t make much sense. So, we should avoid making this error.
Answer choice (B) is already in the base unit, so no conversion is necessary. To apply this process to answer choice (C), we use a conversion factor of one meter
over 100 centimeters. The centimeter units cancel out, giving us a final answer of 10 meters. Using the same conversion factor for choice (D), which is also in centimeters, yields
an answer of one meter. We don’t always have to show the units canceling out, but it can be a convenient way
to ensure that we’ve set up the equation the right way. Finally, our last conversion factor: one meter over 1000 millimeters. Carrying out the arithmetic gives us an answer of 100 meters.
Now that we have converted each of these five lengths into meters, we can clearly see
that the length in answer choice (E), 100000 millimeters, equivalent to 100 meters,
is the greatest length. So, which of the following values has the greatest length? That’s choice (E), 100000 millimeters.
