When you adjust the focal length using the zoom ring, the aperture read out will change for most lenses, this is normal and expected behaviour. It happens as a result of the way the optics move mechanically inside the lens. You can tell which lenses will exhibit this behaviour as their aperture will be listed as a range of values such as the AF-S DX NIKKOR 10-24mm f/3.5-4.5G ED.
A prime lens like the AF Nikkor 14mm f/2.8D ED has one focal length and cannot zoom so will not exhibit this behaviour. Neither will a 'constant aperture' zoom like the AF-S DX Zoom-Nikkor 12-24mm f/4G IF-ED.
Your camera is working as it should, don't worry.
Update: Based on feedback in the comments this is not the problem in this instance as it happens with prime lenses but I'll leave it here as it's likely to be seen by others who are seeing this behaviour.