The only way I'd do that is if the client gave me 10 mins of work one day, followed by 10 mins of work the next and nothing else. Otherwise I'd just work 20 mins and bill an hour. More often however they are giving me 40 hours of work per week and I bill 40 hours, even if not every single hour is doing "focused work", and some of it may be downtime. Just like any employee who gets a salary.
I've been a contractor full time for almost 15 years with dozens of different clients big, small and in between. You tend to get a feel for what clients want and/or need and what they don't. Mostly clients just want help getting work done and as long as you're meeting their deadlines and are pleasant to work with, they don't care that how much time you bill (as long as it's not more than 40 hrs per week).
I'm not advocating for taking advantage of clients, but I am advocating for being realistic with running your own business. If you're only billing 10 min stretches you won't be in business for long. Clients understand this. It's just part of doing business.
I've been a contractor full time for almost 15 years with dozens of different clients big, small and in between. You tend to get a feel for what clients want and/or need and what they don't. Mostly clients just want help getting work done and as long as you're meeting their deadlines and are pleasant to work with, they don't care that how much time you bill (as long as it's not more than 40 hrs per week).
I'm not advocating for taking advantage of clients, but I am advocating for being realistic with running your own business. If you're only billing 10 min stretches you won't be in business for long. Clients understand this. It's just part of doing business.