My calculator gives the value of pi as: 3.14159365359
My calculator give the value of 22/7 (3-1/7) as: 3.14285714286
22/7 has a repeating decimal as the value and, as far as I know, pi goes on forever.
for most purposes in my life - as in drafting a pattern - 22/7 - works well enough for most calculations.
0.00126 - a bit more than one-thousandth of an inch variation will probably work well enough with 'a scant quarter inch' seam