I used to argue with my dad on the matter of precision. My dad is and engineer in education and personality as was his dad and his dad's dad and so on, so I inherited the mentality critical thinking and interest in mechanics, processes and technology of an that such a personality brings (Which sadly doesn't help with personal relationships:).
At one point I had decided I wanted to design my own game engine. I had decided I wanted to use the most precise decimal system I could find in 'cough' VB for storing the locations of points. In the process of designing the basics of the engine I tried to find pi to the most decimals that would fit in the desired unit. I had learned the 22/7 trick from my Drafting instructor but was completely unsatisfied with the accuracy of only 2 decimal points.
My dad asked why I thought I needed any precision beyond two decimal points; in the mechanical engineering world two or three decimals are usually considered accurate enough for almost any consumer products, as anything more precise makes little difference, and just the expansion and contraction of materials alone exceeds the difference such precision would bring.
But I was using a computer and despite what the 1950s and the movie industry hope to tell you, computers are inherently inaccurate at least when it comes to trying to calculate decimal and floating point numbers.
If you use floats for storing points in a world you can move around in, you would find that the precision of the locations of points in the center of the world is quite high, but the farther away you move from the center the less precision you have because the whole number portion of the value is getting filled with the larger numbers sacrificing the precision and storage space of the decimal portion. So at the edge of a large map you could end up with unexpected gaps in your world.
Well, okay if you were to only use integers the gaps could be reduced, but when you want to try to copy the nature of your surroundings you might find you want more precision. The thought might come up to use fixed point, sure it could work but you would have to be very careful with your rounding and your geometry. You also end up with geometry that can look a little blocky depending on the resolution of your values.
But I never got far enough along to be able to see any degradation. So now days, I've stopped caring. Well almost, when I go back and play with old geometry code I am still tempted to write everything as doubles rather than singles, but now I've learned to think processor capacity and the effects on speed too.