Low p-value in test of uniformity of uniformly distributed data? First we generated 10 numbers from a $U(0,1)$ then performed a Kolmogorov Smirnov test for q uniform distribution. Why is the p-value small?
> x=runif(10,0,1)
> x
 [1] 0.37010222 0.19008926 0.02689558 0.43170269 0.03485138 0.89168644 0.42372517 
  0.17899880 0.42714650 0.22280316
> ks.test(x,"punif")

    One-sample Kolmogorov-Smirnov test

data:  x
D = 0.4683, p-value = 0.01567
alternative hypothesis: two-sided

 A: Purely by chance, your values are unusually small -- only one of them is above 0.432.

About one time in 64, you should see a p-value at least as low as this if the data are from a uniform.
Here I generate 1000 such samples of size 10: 
 pvals <- replicate(1000,ks.test(runif(10),"punif")$p.value)

In 15 of those samples, I got p < 0.01567:

which is close to what you'd expect. If 1000 people all do your exercise, you expect about 15 of them to get a p-value as low as that. Your sample is like those. You just happened to have an event that happens about 15.67 times in 1000 by chance.
Once in a while, you could toss a fair coin six times and get six heads. It doesn't mean the coin isn't fair.
A: Here is an image of the estimated density of your sample.

x<-c(0.37010222, 0.19008926, 0.02689558,0.43170269 ,0.03485138, 0.89168644, 0.42372517, 0.17899880, 0.42714650, 0.22280316)
plot(density(x))

From this image, I think it's quite obvious why the p-value is so small. Because the sample that you happened to randomly generate doesn't look very uniform. If your sample size was larger, it would likely look more similar to uniform.
