High School

If there are 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day, 7 days in a week, 4 to 5 weeks in a month, and 12 months in a year, how many seconds are there in a year?

Answer :

There are approximately 31,104,000 seconds in a year, using the average number of weeks in a month.

To calculate the total number of seconds in a year, we can follow a step-by-step approach using the conversions you mentioned. Here is a simplified breakdown:

  1. Calculate seconds in a day:

    • There are 24 hours in a day.

    • Each hour has 60 minutes:

      [tex]1 \text{ day} = 24 \text{ hr} \times 60 \text{ min/hr} \times 60 \text{ s/min} = 86,400 \text{ s/day}[/tex]

  2. Calculate seconds in a week:

    • There are 7 days in a week:

      [tex]1 \text{ week} = 7 \text{ days} \times 86,400 \text{ s/day} = 604,800 \text{ s/week}[/tex]

  3. Estimate seconds in a month:

    • Taking an average of 4.33 weeks in a month (since a month can vary between 4 to 5 weeks), calculate:

      [tex]1 \text{ month} = 4.33 \text{ weeks} \times 604,800 \text{ s/week} = 2,592,000 \text{ s/month}[/tex]

  4. Calculate seconds in a year:

    • There are approximately 12 months in a year:

      [tex]1 \text{ year} = 12 \text{ months} \times 2,592,000 \text{ s/month} = 31,104,000 \text{ s/year}[/tex]

Final answer:

There is a total of 31,536,000 seconds in a common year, calculated by multiplying the number of seconds in a day (86,400 seconds) by the number of days in a year (365). This estimate does not include leap years or leap seconds.

Explanation:

To calculate the total number of seconds in a year, consider the following conversions: 1 day equals 24 hours, 1 hour equals 60 minutes, and 1 minute equals 60 seconds. These conversions allow us to compute the number of seconds in a day, which acts as the building block to calculate the number of seconds in larger time periods, such as a week, a month, and a year. Since a common year has approximately 365 days, using the conversion factors we find:

1 day × 24 hr/day × 60 min/hr × 60 s/min = 86,400 seconds/day.

Therefore, the total number of seconds in one year is:

365 days × 86,400 s/day = 31,536,000 seconds/year.

This calculation doesn't consider leap years, which have an additional day (86,400 seconds). Also, leap seconds are occasionally added to account for Earth's varying rotation speed.

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