Iteration 3

Hence, the root is bracketed between and , that is, between 0.055 and 0.6875. So the lower and upper limit of the new bracket is

The absolute relative approximate error, at the ends of iteration#3 is

Still none of the significant digits are at least correct in the estimated root of the equation as the absolute relative approximate error is greater than 5%.

Seven more iterations were conducted and these iterations are shown in the table below.

Table 1: Root of f(x)=0 as function of number of iterations for bisection method.

Iteration	xl	xu	xm	%	f(xm)
	0.00000 0.055 0.055 0.055 0.06188 0.06188 0.06188 0.06188 0.0623 0.0623	0.11 0.11 0.0825 0.06875 0.06875 0.06531 0.06359 0.06273 0.06273 0.06252	0.055 0.0825 0.06875 0.06188 0.06531 0.06359 0.06273 0.0623 0.06252 0.06241	---------- 33.33 20.00 11.11 5.263 2.702 1.369 0.6896 0.3436 0.1721	6.655x10^-5 -1.622x10^-4 -5.563x10^-5 4.484x10^-6 -2.593x10^-5 -1.0804x10^-5 -3.176x10^-6 6.497x10^-7 -1.264x10^-6 -3.0767x10^-7

At the end of 10^th iteration,

Hence the number of significant digits at least correct is given by the largest value of ‘m’ for which

So

The number of significant digits at least correct in the estimated root of at the end of the iteration is .

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