High precision IMU sensors

Ok, so I got an MPU6050 the other week, pretty happy with it so far. I see 400 microG per hertz as noise in the spec and I assume that's a one way to compare error between various accelerometers?! The lower the number the better. Please correct me if I'm wrong.
What's the most precise accelerometer and/or gyro below say $500? Or even something more precise, less erroneous then the MPU6050. I know there's filtering I can apply, DMPs, I'm simply talking in terms of raw unfiltered data.

Thanks!

Fitting the IMU to the project seems more appropriate. What are your precision requirements?

Does using a $500 IMU with a $30 microcontroller make sense?

PaulS:
Does using a $500 IMU with a $30 microcontroller make sense?

$19.95

Noise is not the same as precision. Precision is not the same as accuracy. Noise measurements are of the power-per-unit-spectrum, back-converted to amplitude (hence the square-root). The noise is actually electrical, but is given in terms of g to make comparing different devices performance easy. The DC-precision might be extremely good even in the midst of lots of noise (you have to low-pass-filter more to remove more noise). Conversely a low-noise device might be very imprecise. The faster you want to measure the more important noise becomes.

Having said that no MEMs IMU chip is that accurate or precise, they are far too small to give highly accurate/precise measurements. Accurate rate-gyros these days are laser-based, accurate accelerometers are basically larger versions of a MEMs device, needing more power. 1 micro-g total noise isn't uncommon from a quick search, < 0.03% linearity, 145dB dynamic range etc etc.

[ quick explanation: in scientific jargon "accuracy" relates to whether the measurement is close to the real value, "precision" relates to how small a step can be recorded consistently by the device (whether or not its accurate). Thus a tape measure with mm markings has a precision of 1mm, even if it happens to be badly stretched and is 5% out! Its accuracy is 5%. In electronics the number of bits from the ADC limits the maximum precision, but a device may be less precise than the number of output bits would suggest (and even less accurate)! ]