When you manage the schedule and budget, you normally do not need to be accurate to the minute or to the dollar. You also do not want make all kinds of proactive changes if your project is a day over deadline one week and a day ahead of schedule the next. Your client does not expect that level of accuracy in your schedule management and they are not interested in knowing whether your project is one hour ahead or behind schedule at any given time.
As the project manager, you should understand the tolerance level for your project. For example, let’s say you are updating your schedule and you realize you have overspent your budget by $1,000. Should you raise an issue or a budget risk? Should you inform your client? It depends on your tolerance level. If you have a $10,000 budget, you should probably be concerned, because you are at risk of going over budget by 10%. If your project has a one million dollar budget, then the thousand dollars is not material at all (in fact you would be a hero if you delivered within $1,000).
Use common sense and work with your client on the tolerance levels for budget and deadline. If you stay within the tolerances, you are fine. If you go outside those limits, you should be concerned.
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