Question

What is the order of magnitude of the number of seconds in one year?

Short answer

Answer: The order of magnitude of the number of seconds in one year is approximately 8.

Step-by-step solution

Calculate the number of seconds in a year

First, we need to find out how many seconds are in a year. We know that: 1 year = 365 days (ignoring leap years) 1 day = 24 hours 1 hour = 60 minutes 1 minute = 60 seconds To find the total number of seconds in a year, we will multiply the number of days in a year by hours, minutes, and seconds: Total seconds = (365 days) × (24 hours/day) × (60 minutes/hour) × (60 seconds/minute)

Calculate the order of magnitude

To find the order of magnitude, we need to express the total number of seconds as a power of 10. We can use the base-10 logarithm to do this: Total seconds = 365 × 24 × 60 × 60 Total seconds ≈ 31,536,000 Now we will find the order of magnitude using the base-10 logarithm: Order of magnitude = log10(31,536,000) ≈ 7.5 Since the order of magnitude should be a whole number, we will round it to the nearest whole number: Order of magnitude ≈ 8 Thus, the order of magnitude of the number of seconds in one year is approximately 8.