MMA8451 Accelerometer Breakout Board Poor Readings? Better Available?

I just bought the Adafruit MMA8451 Accelerometer Breakout Board. I hooked it all up and started to read the output, but it's not as accurate as I thought it would be. The readings are jumping around a lot.

When setting the accelerometer on a table, the gravity acceleration measurement is very jumpy. It goes anywhere from ~9.6 to ~9.9 m/s^2. Is it supposed to be that sporadic? Is there a way to get more accurate and consistent measurements (without any sort of filtering)?

I need the stability because I am trying to measure 0.01 m/s^2 accelerations. If there is a better breakout board available for the +- 6G range, I'm open to suggestions.

120m/s^2 with a resolution og 1/100 ??
sorry, I'm afraid such a sensor in not available for the hobby_marked.

Any vibration/sound nearby will affect the reading. Average several readings for better result

Could you be a little more specific on the G range you really need or the application? I'm trying something with the need for lower range and not the resolution. Thanks. JBB