Prime Minister David Cameron has said he will allow his children to have Facebook accounts - but only if he is able to monitor them.
Mr Cameron said that watching his young children take their first steps into the digital world was one of the factors which prompted him to take action on access to porn on the internet.
But he said that explicit imagery is not the only aspect of the web which concerns him as a parent.
Speaking to Grazia magazine, the Prime Minister said he was worried about children unwittingly running up large bills on online purchases, as well as the consequences for young people of putting too much information onto social media websites like Facebook.
Mr Cameron said he would let Nancy, nine, Arthur, seven, and Florence, two, sign up to Facebook when they are older, describing it as "a way that lots of people communicate" in the modern age, but said he would warn them against anything which might eventually impact on their long-term career prospects.
"All I want is to be able to see their Facebook pages, to start with," said the Prime Minister.
"Now everyone shows their pictures on Facebook, they need to think: well what about that job interview?"
Earlier this month, Mr Cameron announced plans to require internet providers to install porn-blocking filters on new broadband accounts unless customers specifically ask for uncensored access.
He told Grazia that expectations about sex and relationships were being altered because porn was being accessed by children who "aren't old enough to process it properly".
"That has a very corrosive effect: forming relationships is one of the most important things that can happen," he said.
Mr Cameron said that he had already spoken with Nancy about the way in which the media can distort images of women, describing it as "just good advice about judging people by what they do and say and not how they look".
And he said he also worries about his children spending money on in-app purchases, where a game is downloaded for free onto a phone or tablet computer but players can then rack up large bills buying add-on extras, such as additional powers for their on-screen characters.
"You've set up some football game and the next thing you know, you own half of Real Madrid," he joked.
Asked what advice he would give the Duke and Duchess of Cambridge about bringing up their new baby George, Mr Cameron said: "Enjoy it. It's the most magical time."
He said that he was "treasuring every moment" of Florence's early years, as he knew she would be the last child he and wife Samantha have.
"I don't want to single out Florence for praise, but it's such a treat when you know it's the last," he said. "You dote pathetically."