ϵ=1.0;
n = 0.0;
While[(1+ϵ) > 1,ϵ=(2^(-n));n++];
ϵ
n

FindRoot[Sin[x]/x<1,{x,1},WorkingPrecision->10]

h=0.0001;
While[Sin[h]==h,h+= 0.0001];
h