That's a nice, low figure.
But your gut may be telling you that it's worse than that -- especially if you're in a lower income bracket -- because left out of the "core" are food and energy goods, which have continued to climb significantly. (Gut check: been paying more at the pump lately?)
To quote Jeffrey Saut, Chief Strategist of Raymond James, "These inflationary leanings were reflected in last week’s headline CPI figures (+0.7% in May), which were the second highest in 16 years, that is still not being reflected in the laughable “core figures” (+0.1%)".
We could laugh, but the problem is that growth isn't keeping up with real inflation. That's bad news -- some call it "stagflation" (as in: a stagnant economy during a period of real inflation; remember the '70s?) Tough choices for financial policy makers, since one major tool to fight inflation is being able to raise interest rates or keep them high -- but economic growth is stimulated by lower interest rates.
When the Fed meets next week, they'll give more weight to the "Core CPI" than to real inflation. Look for them to keep interest rates high.