Are these vaccines here in the U.S. ineffective since 100+ fully vaccinated people in Washington state have contracted COVID?

The number really doesn't say anything, unless we know how many people in total have been vaccinated in the state, and the timings of these. 

This is like the "chain reaction" used to describe an atom bomb.  All these systems mathematically are the same.  If one person infects more than one person on average then the pandemic will be out of control.  If one person infects LESS than one person on average then it will gradually disappear.  ANYTHING that makes the difference is vital.  Masks.  Social distancing.  Vaccines.  Lock downs.  If the current reinfection rate was 1.3 and you had a vaccine that was 50% effective the rate drops to 0.65 and over five months no more covid.  If you can only drop the reinfection rate to 0.95 then it would take 3 or 4 years to reach the same point.  So everything that helps makes all the difference in the world to the final outcome.

No, or it would have been 2000

I agree with what others have pointed out. While the vaccine is suppose to be 95% effective, there is a 5% infective rate. This means that 5% will still get sick but hopefully not so sick that they will develop respiratory failure and end up on a ventilator. It will prevent severe disease in these patients. 

NO vaccine is EVER 100% effective 100% of the time. That includes these new ones. Even measles vaccine, which has been around for decades, only has an efficacy rate of around 97%. The people that have become infected after getting vaccinated for COVID-19 have had milder cases with far fewer symptoms than they would have had without the vaccine. And the vaccine has kept them OUT OF THE hospital. That means it's working. People occasionally getting reinfected despite vaccination is an expected thing.

Vaccines do not prevent getting the disease in all people.  

The COVID vaccines reduce the symptoms so fewer people end up in hospital or dying.  Some people will get a very mild case.

In Washington state, almost 3,326,000 vaccines have been given.  So if we assume that is 2 doses per person, that works out to 1,663,000 people fully vaccinated.

If 100 of those people get the virus, that means it is 99.4% effective in preventing the disease.

Some people really need to do some thinking before reacting.

Before being approved for widespread use, both the Moderna and Pfizer vaccines were shown to be over 94% effective in clinical trials. But people seem to ignore the fact that those effectiveness figures also mean that for every 100 vaccinated people, approximately 6 people will still get Covid. 

So it's not surprising to learn that some fully vaccinated people are still contracting Covid. It is, in fact, expected.

Remember, no vaccine is 100% effective. Indeed, most vaccines historically fail to show greater than 70% effectiveness. That makes these newly developed Covid vaccines some of the most effective vaccines ever developed.

Documentation please.  

they dont sound like they are

The vaccines are just microchips that track you at all times! There is no COVID!