I start with 54 liters and 3.41 cubic microns per minute. I want an answer in seconds.
So [MATH] 51 \text { liters combined somehow with } 3.41 \text { cubic microns per minute} = x \text { seconds.}[/MATH]
Now with very rare exceptions, these conversion problems just involve multiplication and division. I see my answer in units of time, namely seconds. But my time unit on the left is in minutes. Easy peasy. We will multiply by
[MATH]\dfrac{60 \text { seconds}}{\text {minute}}[/MATH].
Does that make sense?
But wait a minute. If we multiply
[MATH]\dfrac{3.41 \text { cubic microns}}{\text {minute}} * \dfrac{60 \text { seconds}}{\text { minute}}[/MATH]
we are going to end up with an answer in seconds per square minute, and that makes no sense at all. So we should multiply by the reciprocal of 3.41 cubic microns per minute. Let’s see whether that makes sense.
[MATH]\dfrac{\text{ minute}}{3.41 \text { cubic microns}} * \dfrac{60 \text { seconds}}{\text { minute}}[/MATH].
The minutes cancel. That looks good. But we can see something else. Liters and cubic microns are both measures of volume. But we don’t want any volume units in our answer. Since cubic microns are in the denominator, liters must be in the numerator for the volume units to ultimately cancel. So we can see that we are going to end up with some thing like this
[MATH] \dfrac{51 \text { liters}}{1} * \text {some metric volume conversion} * \dfrac{\cancel {\text {minute}}}{3.41 \text { cubic microns}} * \dfrac{60 \text { seconds}}{\cancel{\text{minute}}} = x \text { seconds.} \implies[/MATH]
[MATH]\dfrac{51 * 60 \text { seconds}}{3.41} * \dfrac{\text {liter}}{\text {cubic micron}} * \text {some metric volume conversion} = x \text { seconds.}[/MATH]
