How would you use Newton's Method without a calculator, if you are for example asked to to find a solution correct to 3 decimal places? I can only do it as a fraction, and my exam coming up soon and we not allowed to use calculators.

Use Newton's method with the specified initial approximation x1 to find x3, the third approximation to the root of the given equation. (Give your answer to four decimal places):

Yeah I got that, then I found x3 to be 932/790, but not sure of an efficient way of showing it to 4 decimal places without a calculator, besides using long division (which may indeed be very long lol)