Because Earth's rotation is gradually slowing, the length of each day increases: The day at the end of 1.0 century is 1.0 ms longer than the day at the start of the century. In 58 centuries, what is the total (in hours) of the daily increases in time (that is, the sum of the gain on the first day, the gain on the second day, etc.)?

To calculate the total increase in time over 58 centuries, we need to find the sum of the daily gains.

Given that the day at the end of 1 century is 1.0 ms longer than the day at the start of the century, we know that the daily gain is 1.0 ms / 100 years.

To convert this daily gain from milliseconds to hours, we need to divide it by the number of milliseconds in an hour. There are 60 seconds in a minute, 60 minutes in an hour, and 1,000 milliseconds in a second. So, the conversion factor is (1 hour / 3,600,000 ms).

Now, we can calculate the daily gain in hours:

1.0 ms / 100 years * (1 hour / 3,600,000 ms) = 0.00000027778 hours

This means that each day increases by approximately 0.00000027778 hours.

To find the total increase in time over 58 centuries, we multiply the daily gain by the number of days in 58 centuries.

There are 100 years in a century, and assuming each year has 365 days (ignoring leap years), we have:

58 centuries * 100 years/century * 365 days/year = 2,102,000 days

Finally, we can calculate the total increase in time (in hours):

0.00000027778 hours/day * 2,102,000 days = 0.5822222 hours

Therefore, the total increase in time over 58 centuries is approximately 0.5822222 hours.

To find the total increase in time over 58 centuries, we need to calculate the total number of days in 58 centuries and then convert it to hours.

1. First, let's calculate the number of days in 58 centuries.

One century consists of 100 years. So, 58 centuries would be equal to 58 * 100 = 5800 years.

2. Next, let's calculate the number of days in 5800 years.

We know that there are 365 days in a year. Considering leap years, there is an average of 365.25 days in a year. So, the total number of days in 5800 years would be 5800 * 365.25 = 2,117,700 days.

3. Now, we need to convert the total number of days to hours.

There are 24 hours in a day. Therefore, the total number of hours in 2,117,700 days would be 2,117,700 * 24 = 50,826,000 hours.

So, the total increase in time over 58 centuries is 50,826,000 hours.