Client gives you a 10 minute task. Do you charge your client half hour or full hour. Client is not retaining you full time, pays you as 1099 contractor, and offers no benefits.
This is a semi-open-ended question as it's really up to you how you charge for your time but -
Does it make sense to charge for an hour after 10 minutes of your time? No. If I hire a freelancer because I have an issue that I can't figure out how to solve and they charge $100/hour I'm not going to ever want to work with them again if after a 10 minute fix/training I receive a bill for $100, I wouldn't even be happy with a $50 bill for something so trivial as 10 minutes.
However, this should be defined within a contract as to how you charge. I do have a payment model much like the above for video consultations. I give those clients a 1 hour monthly consultation about digital marketing or web development and my contract states that I will charge them the full 1 hour if the call lasts more than 30 minutes and I'll charge 55% for a call under 30 minutes. This is signed and agreed upon.
Without a contract it's up to you but keep in mind they can contest a payment if they expect to recieve a bill for (let's say) $10 and you send them one for $100. Do you plan on working with them in the future? Do you want to risk a contested payment?
Personally, If I wasn't using a time tracker through their project management system I would charge within 1/4 hour rates if there's no contract. For 10 minutes of my time I'll charge for 1/4 of an hour. That makes it easier on myself so I'm not charging dollars and pennies for things like 8 minutes, 13 minutes, etc.
This is why having a contract is important so that both parties understand payment terms.