If someone asks you, "How old are you this year?" and you reply, "I'm 15 years old," this answer is correct, but 15 is just an approximate value of your age, not an exact one. If your friend is also 15 years old and you want to compare your ages, you need to know the exact months when you were born. In other words, you should say that you are 15 years and a few months old to make the comparison, but it's still an approximation. If both of you were born in October, then you must know the exact dates of your birthdays, that is, you should specify your age as 15 years and a few months and days to determine which of you is older. If they are twin sisters, then the older sister is only a few hours or minutes older than the younger one, and to compare their ages, you need to specify their ages in years, months, days, and even seconds and minutes.
One minute can be divided into 60 seconds, and one second can be further divided into 1/10 seconds, 1/100 seconds, and 1/1000 seconds, and so on indefinitely. However, there's no need to be this precise about our age. Usually, it's enough to just give an approximate value - how old you are. Measuring height is generally accurate to centimeters, while engineering drawing requires relatively high accuracy. However, in many scientific problems, it's necessary to be very precise about time. The "beep... beep..." time signal we hear on the radio every hour is only a few thousandths of a second behind the actual accurate time. Oceangoing ships use this signal to determine their position. In atomic physics, the lifetime of a "hyperon" is only 10-10^ to 10-8^ seconds, which is extremely short. To determine their age, it's necessary to be accurate to at least 10-10^ to 10-8^ seconds.
Therefore, the moments we usually talk about are all approximations, some more accurate and some less. As for how precise it should be, it depends on the needs of the actual problem. There's no need to be precise to seconds when talking about people's ages; however, if we're only accurate to seconds for "hyperons," we won't be able to measure their real lifespan. Therefore, the accuracy of measurement varies among different problems. Let's think about it - when it comes to length, would the accuracy required for measuring height be the same as that for measuring the length of a highway?