Sector giants BHP Group BHP.AX, Rio Tinto RIO.AX and Fortescue Metals Group FMG.AX added between 0.3% and 0.6%. Jan 13 (Reuters) - Australian shares rose on Friday, on track for their best weekly gain in nine, as positive U.S. economic data signalled easing inflation, raising investors' hopes for a pivot on policy tightening by the Federal Reserve. Data showed that U.S. consumer prices fell for the first time in over 2-1/2 years last month, indicating that inflation was now on a sustained downward trend, boosting the case for the central bank to ease off from its hawkish monetary policy.