Pam Alnwick used to live in a province where the Harmonized Sales Tax, HST, was 16%. She recently moved to state in the US where sales tax is 6.7%. When shopping, the task of comparing American prices with Canadian prices was further complicated by the fact that, at the time of her move, the Canadian dollar was worth 0.78US$. After thinking about it, she calculated a number K so that a pre-tax shelf price of A US$ could be sensibly compared with a pre-tax shelf price of C CDN$, so as to take into account the different sales tax rates. Her K had the property that if AK=C, then the after-tax costs in Canadian dollars were the same, while if AK is less (greater) than C, then, after taxes, the American (Canadian) price is cheaper. Find Pam's multiplier K.

Pam's multiplier K is ______. (Integer or decimal rounded to four decimal places as needed)