Problem 4 Solution
Regular notation: 31557600 seconds per year, rounded to 5 digits gives 3.1558 x 107 seconds.
Solution Steps for Problem 4The key: Multiply by the number of seconds per minute.
Note 1: If you start with your answer from problem 3, and you only have 4 significant digits in the number of minutes per year, and you only have 2 significant digits in the number of seconds per minute (60), perhaps we should only use 2 significant digits in this answer. We are using 5 since the number of seconds in a minute is a definition and not a measurement, as is the number of minutes in an hour, and the number of hours in a day. But the number of days in a year is a measurement, since we measure (observe) it as the time it takes the earth to round the sun. So with 5 significant digits in the days per year, and 5 significant digits in the seconds per day, we could multiply these two numbers and get the results above.
Note 2: A Curious Approximation: Many scientists have used the approximation that there are "Pi times ten to the seventh" seconds in a year. Looking at the answers above, can you see why this is a good approximation? How good is it?
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