At what level of granularity is a client required to pay

Question

This is more of a thought experiment more than anything else. But let's say for argument's sake that a client had a contract in place with a worker for 100/hr. And also for argument's sake, the worker is a bit cheeky and decides to charge the client for work down to the level of seconds. The worker also has verifiable logs of every second work.

If the worker charged for 1hr 12 min 39 seconds, and the client refused to pay for more than the hour, what would happen? Would the judge simply throw it out? Is there some merit to the hypothetical worker's case?

EDIT: Answer for the US Jurisdiction for which you are most familiar

Answer 1

If this is a client - contractor relationship, it depends on the contract. Attorneys may bill on a quarter-hour basis, or a 10th-hour basis. A 1 minute phone call under a quarter hour billing basis is more expensive than under a 10th-hour basis, all other things being equal (i.e. the hourly rare). So if I hire an attorney to do something and he bills me for 1 hr 6 minutes because he spent 1 hr 4 minutes to do it, he can do that, and I can't object that he didn't spend a full second hour on the task. It just comes down to what the client and contractor agreed to, and if a contractor wants to bill by the second, he can.

For employers and their employees, the Fair Labor Standards Act applies in the US (there are state analogs which mostly say the same thing). The employer is responsible for paying employees based on work done, so they have to keep records. Department of Labor rules allow an employer to simplify record keeping, for example they can round employee hours (1 hr 2 minutes is the same as 55 minutes) – you have to be consistent. They explicitly allow 5 minute granularity, and don't disallow granularity to the second.

Answer 2

Assuming that this is a contractor relationship, not en employee/employer relationship, the contract would control. If the contract fails to specify, then "usual and customary" practice in the industry or type of contract would control. As mentioned in a comment, many lawyers bill in 1/4 hr or 1/10th hr increments, so it would be acceptable to use either of those. In some other fields, billing is typically by the 1/2 hr or hour, and in some by the day. Note that in most fields overage allows for billing the next increment, so if the contractor worked 1hr 12 min 39 seconds billed on an hourly basis, the bill could legitimately be for 2 hours, not 1.

In the case of an employment relationship, I have nothing to add to the answer by @user6726.