The IRS probably would not consider the whole day as uninterrupted business use unless you could prove that the entire day was, in fact, spent driving passengers around. If you stopped off somewhere for lunch in between rides, and that was your only non-business stop of the day, you could possibly consider your entire day as uninterrupted business use, so long as your lunch stop wasn't a significant part of your day. However, not keeping track of your actual business miles is not a good idea, because the IRS may not allow you to deduct any of your mileage expenses if they feel you don't have sufficient proof that you spent your entire day driving passengers around. Each passenger ride you provide should be its own trip with its own mileage tracking. However, you can deduct all of the miles that you drive to pick up your passengers, the miles you drive with your passengers in the car, and the miles that you drive if you drop off all your passengers and have to drive elsewhere to pick up more.
The best way to ensure you accurately report all the business miles you drive would be to use an app or odometer to log the mileage you drive with passengers in the car, the mileage you drive to pick up passengers, and the mileage you drive between one passenger and another. If you want to use the odometer to log your miles, you could keep a journal and write the number on the odometer at the start of each trip and the number on the odometer at the end of each trip. Subtracting the starting number from the ending number would give you the total mileage for that trip, and the journal could help serve as proof of your miles if the IRS ever audited your return. However, I do not recommend this method, as using a journal to track mileage would be tedious and also waste time and paper. Instead, I would recommend using an app that allows you to log mileage, as the app's records would not only make it easy to track your miles, but would help prove the accuracy of your miles to the IRS. Here is a list of apps that make it easy to log your business mileage so you can efficiently and accurately keep track of your mileage.
When you go to deduct your mileage expenses on your tax return, you can do so on Schedule C (Part II, Line 9). The easiest way to calculate the cost of your miles is to use the IRS standard mileage rate, which for 2020 is 57.5 cents per mile. For example, if you logged 10,000 miles in your app for 2020, your mileage expense for Schedule C would be $5,750 (10,000 miles times $0.575 per mile). You could also use the actual expense method to calculate the cost of your mileage, but that method is significantly more detailed and complex than the standard mileage rate. However, it is entirely up to you which method you would like to use, and you don't have to use the same method every year.
In summary, the easiest way to keep track of your daily miles is to use an app that makes it easy to record your miles and then multiply all your miles for 2020 by the standard mileage rate. It's always a good idea to consult a tax professional if you have any questions on how to file a Schedule C or how to properly report the miles you log.