Why are resistors and capacitors usually available only in certain denominations?

Anyone interested in hobby electronics would have noted that resistor values follow a certain pattern. For example, you would have noted resistors of 220 Ohms, 330 Ohms, 470 Ohms, 2.2 K, 3.3K, 4.7K, 22K, 33K, 47K etc. I have always wondered why in this pattern rather than better round numbers. The reason lies in a logarithmic scale depending on the tolerance value of the resistors so that manufacturers need only make a fixed set of values and suppliers need stock only them. This also allows engineers designing circuits to go for only the standard values rather than using random values in circuits. These set of values are called the preferred values or E-series. You would have noted same pattern being followed by capacitors as well.

In the most commonly used E-12 series meant for resistors with 10% tolerance or variability in the value uses 12 steps in each decade like between 1-10, 10-100 and 100-100 or even lower fractions. The calculation of values is based on  10 to the power of 1/12, which becomes multiples of 1.21. That is actually a logarithmic scale dividing steps in a decade. 10% upper tolerance value of the lower series will overlap with the 10% lower value of the upper series. That is how the scale has been arrived at, so that there is no point in making values in between. Similarly, there are E6 series of values for resistors with 20% tolerance. On the higher end of precision, there are other series, with even E192 series for tolerance 0.5%, 0.25% and 0.1%!