91Ó°ÊÓ

We are given the cross-sectional area of the capillary in square micrometers: \(150\, \mu\mathrm{m}^2\).

To convert the given area to square millimeters, we must first find the conversion factor from square micrometers to square millimeters. Recall that 1 micrometer (\(\mu\mathrm{m}\)) is equal to \(10^{-6}\) meters and 1 millimeter (\(\mathrm{mm}\)) is equal to \(10^{-3}\) meters. So, we can write: $$1\, \mu\mathrm{m} = 10^{-6}\, \mathrm{m}$$ To convert square micrometers to square millimeters, we should square both sides: $$(1\, \mu\mathrm{m})^2 = (10^{-6}\, \mathrm{m})^2$$ $$1\, \mu\mathrm{m}^2 = 10^{-12}\, \mathrm{m}^2$$ Next, we can convert the result to square millimeters by dividing it by the square of the conversion factor between millimeters and meters: $$\frac{10^{-12}\, \mathrm{m}^2}{(10^{-3}\, \mathrm{m})^2} = \frac{10^{-12}}{10^{-6}} \mathrm{mm}^2$$ $$1\, \mu\mathrm{m}^2 = 10^{-6}\, \mathrm{mm}^2$$

Now we can multiply the given area in square micrometers by the conversion factor calculated in Step 2: $$150\, \mu\mathrm{m}^2 \cdot 10^{-6}\, \frac{\mathrm{mm}^2}{\mu\mathrm{m}^2} = 150 \times 10^{-6}\, \mathrm{mm}^2$$

Finally, perform the multiplication and simplify the result: $$150 \times 10^{-6}\, \mathrm{mm}^2 = 1.5 \times 10^{-4}\, \mathrm{mm}^2$$ So, the cross-sectional area of the capillary in square millimeters is \(1.5 \times 10^{-4}\, \mathrm{mm}^2\).