Source: Extra Practice

What is the order of magnitude of the number of seconds in a day?

Options

Option A

10310^3

Option B

10410^4

Option C is correct

10510^5

Option D

10610^6

Explanation

First, calculate the total number of seconds in a day: Seconds in a minute = 60 Minutes in an hour = 60 Hours in a day = 24 Total seconds in a day = 24×60×60=8640024 \times 60 \times 60 = 86400 seconds. To find the order of magnitude, express the number in scientific notation: 86400=8.64×10486400 = 8.64 \times 10^4. For a number written as N×10pN \times 10^p, where 1N<101 \le N < 10, the order of magnitude is 10p10^p if N103.16N \sqrt{10} \approx 3.16, we round up the power of 10. Therefore, the order of magnitude is 104+1=10510^{4+1} = 10^5.