For a number too large to write down in the Conway chained arrow notation we can describe how large it is by the length of that chain, for example only using elements 10 in the chain; in other words, we specify its position in the sequence 10, 10→10, 10→10→10, .. If even the position in the sequence is a large number we can apply the same techniques again for that. Numbers expressible in decimal notation:  Numbers expressible in scientific notation:  Numbers expressible in (10 ↑)"n" "k" notation:  Bigger numbers:  The following illustrates the effect of a base different from 10, base 100. It also illustrates representations of numbers and the arithmetic.  formula_124, with base 10 the exponent is doubled.  formula_125, ditto.  formula_126, the highest exponent is very little more than doubled (increased by log102). For a number formula_145, one unit change in "n" changes the result by a factor 10. In a number like formula_146, with the 6.2 the result of proper rounding using significant figures, the true value of the exponent may be 50 less or 50 more. Hence the result may be a factor formula_147 too large or too small. This seems like extremely poor accuracy, but for such a large number it may be considered fair (a large error in a large number may be "relatively small" and therefore acceptable). In the case of an approximation of an extremely large number, the relative error may be large, yet there may still be a sense in which we want to consider the numbers as "close in magnitude". For example, consider  The relative error is  a large relative error. However, we can also consider the relative error in the logarithms; in this case, the logarithms (to base 10) are 10 and 9, so the relative error in the logarithms is only 10%. The point is that exponential functions magnify relative errors greatly – if "a" and "b" have a small relative error,  the relative error is larger, and  will have an even larger relative error. The question then becomes: on which level of iterated logarithms do we wish to compare two numbers? There is a sense in which we may want to consider  to be "close in magnitude". The relative error between these two numbers is large, and the relative error between their logarithms is still large; however, the relative error in their second-iterated logarithms is small:  Such comparisons of iterated logarithms are common, e.g., in analytic number theory.