According to spec, EXIF stores latitude and longitude with 192 precision each. But a simple calculation shows that you only need 32 bits to divide the circumference of Earth into segments of 9 mm:
r = 6378 km = 6.378 × 10^6 m
C = 2πr = 4.007 × 10^6 m
stepSize = C / 2^32 = 0.009 m = 9 mm
That's assuming you store the data in steps of equal size, so as an unsigned int. I can understand that would make handling code harder to write, so what the hell: let's use a double. At this precision, we can divide the Earth's circumference into steps of 2 picometers. A Helium atom has a diameter of 62 picometers. So at 64 bits, we have enough precision to divide the Earth's surface at subatomic scales.
What on Earth do we need 192 bits per angle?
The format stores latitude and longitude each as 6 32-bit integer values, which adds up to 192 bits. The 6 integers store each of degrees, minutes and seconds as rational numbers with a numerator and denominator.
Why this format? Presumably it's designed for very simple processors that can't handle floating point, and might not even be able to do division. The format is more than 25 years old (though I'm not sure when GPS data was added), and cameras weren't as smart back then. Cameras needed to be able to store lots of data (pictures are big), but they didn't need to do a lot of mathematical operations on it. So they wasted some bits to make manipulation easier.