Use integers, calculate in pennies. So Pi=314 if your internal math is in hundredths or "pennies". Or if you use millimeters instead of meters, pi=3141 What we did 30 years ago on desktops is what embedded hardware still does today... The endless wheel of IT eternally rotates the same concepts back to the top, if you wait long enough.
Another classic is the old hard science error analysis. Lets say you're squaring the radius and multiplying by pi, turns out you need to measure the radius much more accurately than you measure pi, so pi=4 might not be the limiting factor if R is a 8 bit A/D converter and you're not taking full advantage of the entire 8 bit range (so its really a 4 bit a/d or whatever)
Another is systemic effects. Some weird hydraulic PLC thing I was messing with probably 20 years ago basically needed the ratios of areas of circles, and it turns out that any approximation of pi divided by itself always equals 1. The puzzler is for diagnostic purposes they used pi=4 so the numbers kinda made sense in the debugger before the ratio was calculated. I must have thought about that 4 for an hour trying to reverse engineer what they were trying to do before I realized that "4" was their pi approximation and it didn't matter anyway.
If we're on embedded hardware, or can't use floats for some reason, we use 22/7. It's called fixed point arithmetic. Most CPUs have an integer instruction that multiplies into a double-precision integer result, and an instruction that takes a double-precision integer dividend.
So to scale by pi, we multiply by 355, then divide by 113.
