8.99*10^98.99109 seconds is how many years?

1 Answer
Sep 7, 2016

"285 years"285 years

Explanation:

Your strategy here will be to use a series of conversion factors to take you from

  • seconds to minutes

"1 minute " = " 60s seconds"1 minute = 60s seconds

  • minutes to hours

"1 hour " = " 60 minutes"1 hour = 60 minutes

  • hours to days

"1 day " = " 24 hours"1 day = 24 hours

  • days to years

"1 year " = " 365.25 days"1 year = 365.25 days

The last conversion factor doesn't use a whole number because once every 44 years we have what is called a leap year, which means that instead of 365365 days, the number of days we have in a regular year, we get 366366 days.

So, use the conversion factors to find

8.99 * 10^9 color(red)(cancel(color(black)("s"))) * (1color(red)(cancel(color(black)("min"))))/(60color(red)(cancel(color(black)("s")))) * (1color(red)(cancel(color(black)("hr"))))/(60color(red)(cancel(color(black)("min")))) * (1 color(red)(cancel(color(black)("day"))))/(24color(red)(cancel(color(black)("hr")))) * "1 year"/(365.25color(red)(cancel(color(black)("days"))))

=2.85 * 10^2"years" = "285 years"

The answer is rounded to three sig figs, the number of sig figs you have for 8.99 * 10^9 seconds.