What was found
IN CRUISE OVER A THREE HOUR PERIOD #1 MAIN TANK FUEL INDICATION DROPPED FROM 8.62 DOWN TO 8.35. #2 MAIN TANK REMAINED FULL. CROSS FEED FUNCTION NORMAL. RAMP FUEL IN LIH WAS 41.5 WITH BOTH MAIN TANKS FULL AND THE REMAINING FUEL IN CENTER TANK. FF ON #1 ENGINE WAS HIGHER WHEN CENTER TANK WAS EMPTY, IMBALANCE WENT FROM 300-400 LBS. FUEL BALANCE WAS NORMAL AS WELL AS OVERALL FUEL BURN THROUGHOUT THE FLIGHT. GROUNDED - YES. ACCOMPLISHED FQIS BITE REF B737-800 FIM 28-41 TASK 801 NO FLT FAULTS AND GND TEST PASS, CURRENT STATUS NO FAULTS. VERIFIED #1 AND #2 FUEL QTY'S MATCH USING ALTERNATE FUEL STICK METHOD, WING GAGES AND FLT DECK GAGES.