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If I have a resistor with 100 volts applied to it with a resistance of 100 $\Omega$, then the resistor would dissipate 100W. What is the color branding?

My first thought, following the table was, 1 - 0 - 0. So brown-brown. But on Wikipedia (scroll down)

http://en.wikipedia.org/wiki/Electronic_color_code

It says for a 68ohm resistor, the color branding is blue-gray - black - gold.

How does the black cancel out the $10^{6}$ multiplier?

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you should read the link you posted more carefully. For the example you cite, the first three bands are "1st sig. digit (6), second sig. digit (8), multiplier (1)". There is no 10^6 multiplier, since that would require a blue band in the third position. – wsc Sep 8 '12 at 23:21
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As this looks like it actually revolves around a misunderstanding of how to read the resistor coding you might want to have a look at the electronics stack exchange site. – dmckee♦ Sep 8 '12 at 23:56

closed as off topic by Qmechanic♦, David Zaslavsky♦ Sep 9 '12 at 3:22

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