FUEL GAUGE ERROR RESULTING IN ACFT DEPARTING WITH LESS THAN DISPATCH FUEL BOARDED.

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F/O TOTALED THE GAUGES AT 24300#. ACCORDING TO THE FUEL SLIP; THE FUELER ADDED 2481 GALS TO THE 7200# SHOWING ON BOARD GIVING HIM A TOTAL OF 24200#. SHORTLY BEFORE DEP; F/O NOTICED THE #1 FUEL GAUGE FLASHING ALTERNATELY BTWN ERROR CODES 2; 3; 4 AND 6 AND 10200#. HE CALLED A MECH. HOWEVER; WHEN THE MECH AND I ARRIVED; THE GAUGE WAS AGAIN SHOWING 10200#. AS THE GAUGES APPEARED NORMAL AT THIS TIME; AND I WAS CONFIDENT THAT WE HAD THE CORRECT AMOUNT OF FUEL ON BOARD; I DECIDED TO DEPART. IF THE PROB REOCCURRED ENRTE; I WOULD WRITE UP THE PROB IN HOU. AFTER TKOF WE NOTICED THAT #1 GAUGE WAS SHOWING ABOUT 8000 LBS OR 2000# LESS THAN #2 GAUGE. WE WERE BURNING OUT OF THE #3 TANK AT THAT TIME. I ALSO NOTED THAT F/O; WHO WAS FLYING; WAS HAVING TO ADD LEFT RUDDER TRIM TO KEEP THAT ACFT FLYING STRAIGHT. THIS INDICATED THAT THE RIGHT WING WAS HEAVIER THAN THE LEFT WING. TO TEST MY ASSUMPTION; I STOPPED BURNING OUT OF #3 TANK AND BURNED THE RIGHT WING TANK (#2) UNTIL ITS GAUGE SHOWED EQUAL TO #1 GAUGE. NEXT I ADDED THE FUEL SHOWING ON THE GAUGES TO THE FUEL SHOWING ON THE FUEL USED COUNTERS. THIS GAVE ME A FIGURE OF 21500# RATHER THAN THE 24200# SHOWING ON THE FUEL SLIP. WHEN I MADE RADIO CONTACT WITH DEN; I ASKED MAINT FOR ANY SUGGESTIONS. THEY SAID THAT W/O DIVERTING TO DEN; THEY COULD NOT HELP. FROM MY CALCULATIONS; I ESTIMATED THAT WE WOULD LAND IN IAH WITH 2500-3000# OF FUEL. AS RESERVES ARE 4000# AND AS I FELT THAT I COULD NO LONGER TRUST MY FUEL GAUGES; I REQUESTED DISPATCH TO DIVERT TO DFW. WE ARRIVED IN DFW WITH 4500# SHOWING ON THE GAUGES. WHEN MAINT USED THE DIP STICK METHOD; THEY FOUND 5100 LBS ON BOARD. THEY THEN TRANSFERRED ALL THE REMAINING FUEL TO THE CENTER TANK AND ADDED 750 GALS TO EACH WING TANK. THE #1 GAUGE SHOWED 5000 LBS AND THE #2 GAUGE 4850#. WE THEN DEPARTED TO IAH WITH NO FURTHER INCIDENT.