Key Fed inflation measure rose 0.6% in January, more than expected

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3. The expectations don't make sense to me

I don't see how the numbers work. For the year they expected inflation to be 4.4% or a factor of 1.044, instead it was 4.7% or a factor of 1.047. They also expected that the month would be 0.5% or a factor of 1.005 and instead it was 0.6% or 1.006. Here is the problem. 1.047/1/006 = 1.041 which wen multiplied by 1.005 is 1.0459 which isn't 4.4% it is instead almost 4.6%. In other words given what already happened in the previous 11 months, there is no way all of these expectations can be accurate. Either the rate could have been 0.5% last month or the rate for the year could have been 4.4% but not both.