resistors - Why are the E-series numbers different from the powers of 10?

The E-series numbers are the common values used in resistors. For example, the E6 values are:

• 1.0


• 1.5


• 2.2


• 3.3


• 4.7


• 6.8

As you can see, each is about \$10^\frac16\$ apart. But I wonder why they aren't the powers of \$10^\frac16\$ rounded to 2 significant figures.

• \$10^\frac16 \approx 1.4678\$



• \$10^\frac26 \approx 2.1544\$


• \$10^\frac36 \approx 3.1623\$


• \$10^\frac46 \approx 4.6416\$


• \$10^\frac56 \approx 6.8129\$

3.1623 should't round to 3.3 no matter rounding upwards or downwards. And by rounding to the closest number, 4.6416 rounds to 4.6.

The same happens in other E-series values. For example, the powers of \$10^\frac{1}{12}\$ rounded to 2 significant figures are:

• \$10^\frac{0}{12} \approx 1.0\$


• \$10^\frac{1}{12} \approx 1.2\$



• \$10^\frac{2}{12} \approx 1.5\$


• \$10^\frac{3}{12} \approx 1.8\$


• \$10^\frac{4}{12} \approx 2.2\$


• \$10^\frac{5}{12} \approx 2.6\$


• \$10^\frac{6}{12} \approx 3.2\$


• \$10^\frac{7}{12} \approx 3.8\$


• \$10^\frac{8}{12} \approx 4.6\$


• \$10^\frac{9}{12} \approx 5.6\$


• \$10^\frac{10}{12} \approx 6.8\$


• \$10^\frac{11}{12} \approx 8.3\$

While the E12 values are:

• 1.0


• 1.2


• 1.5


• 1.8


• 2.2


• 2.7


• 3.3



• 3.9


• 4.7


• 5.6


• 6.8


• 8.2

The numbers 2.7, 3.3, 3.9, 4.7, and 8.2 from E12 are different from their corresponding ones computed above.

So why are the E-series of preferred numbers different from the powers of 10 rounded to the closest number?