Approximation of Natural Log

Taking the Taylor series of ln(1+x) about x=0 gives the following result, as demonstrated by the MATLAB line:

>> syms x;
>> taylor(log(1+x))
ans =
x^5/5 - x^4/4 + x^3/3 - x^2/2 + x

The common approximation is that as long as x is small, ln(1+x) ~= x. How close is this approximation anyways? In the following Excel table, various small and incrementing values of x were chosen, along with the actual ln(1+x) values. In all cases, the approximation yields a slightly higher answer, since the most significant term of -x^2 was left out. The difference and the % error to the actual values were calculated:

x	ln(1+x)	+ / -	% Error
0.000	0.00000	0.00000	#DIV/0!
0.005	0.00499	0.00001	0.250%
0.010	0.00995	0.00005	0.499%
0.015	0.01489	0.00011	0.748%
0.020	0.01980	0.00020	0.997%
0.025	0.02469	0.00031	1.245%
0.030	0.02956	0.00044	1.493%
0.035	0.03440	0.00060	1.740%
0.040	0.03922	0.00078	1.987%
0.045	0.04402	0.00098	2.233%
0.050	0.04879	0.00121	2.480%
0.075	0.07232	0.00268	3.705%
0.100	0.09531	0.00469	4.921%
0.200	0.18232	0.01768	9.696%
0.300	0.26236	0.03764	14.345%
0.400	0.33647	0.06353	18.881%
0.500	0.40547	0.09453	23.315%
0.750	0.55962	0.19038	34.021%
1.000	0.69315	0.30685	44.270%

Observing for x is 0.05 or smaller, it seems as though the absolute error grows in a quadratic manner, while the percentage error grows constantly. But most importantly, if the approximation of ln(1+x) = x wants to stay within 5% of the actual answer, the value of x shouldn't exceed 0.1.