not so easy #1

Without a calculator, you need to know the first several digits of $1/7$ and of $\pi.$ Since $22/7$ and $\pi$ are both between $3$ and $4,$ the ones digit is $0.$ From there, $22/7 \text{ mod } 1 = 1/7 \\ \approx .14285714...$ $\pi \text{ mod } 1 \approx .14159265...$ $d \approx .14285714 - .14159265 \\ = .00126449 \\ \approx \boxed{0.00126}$