The problems with the petitions on the Number 10 website is that they don't give a balanced view of public opinion. In order to achieve that they need to give you the option to vote for or against the petition. To pick a number out of the ether, 10,000 signatures may seem like a lot, but as a measure of public opinion it means nothing until you find out how many people are opposed. 5 signatures against would give you an idea that the public were pretty much in favour of the proposal, 5,000 could indicate otherwise, 50,000 against would be another matter altogether.
Until we are given the oportunity to sign up against these petitions they are meaningless.