How big (in mm) would a red blood cell 7 µm in diameter appear when viewed? The eyepiece lens of a microscope has a magnification of 10X and an...

A compound microscope has two spherical lenses which work together to magnify the view of an object. The microscope's eyepiece or ocular is the top lens. It usually  has a magnification of 10X, as in this example. It will make the object appear 10 times larger. The objective, which is the second lens, makes the object appear 40 times larger. The total magnification is (10X)(40X) = 400x. 

7 µm x 400 = 2800 µm

Now to convert this to millimeters:

There are 1000 mm in a meter, and 10^6 µm in a meter.

(2800 µm)(1 m/10^6 µm)(1000 mm/1 m) = 2.8 mm

The red blood cell will appear to be 2.8 mm in diameter.

To find the total magnification of a compound microscope you always multiply the magnification of the eyepiece by that of the objective. Most microscopes have three or four objectives that are successively rotated into position to increase the magnification. The total magnification will depend on the objective that's being used.