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

The correct option is 5.

To find the order of magnitude of seconds in a day, we first calculate the total number of seconds in a single day.
A day consists of 24 hours, each hour has 60 minutes, and each minute has 60 seconds. Therefore, the total number of seconds in a day is:

$$N=24\times 60\times 60$$

Calculating this product gives:

$$N=86,400\text{ seconds}$$

To find the order of magnitude, we write the number in scientific notation:

$$N=8.64\times {10}^4$$

The order of magnitude is determined by rounding the pre-factor to the nearest power of 10.
Since the value 8.64 is greater than the square root of 10 (which is approximately 3.16), we round the pre-factor up to 10 (or 10¹).

$$8.64\times {10}^4\approx {10}^1\times {10}^4={10}^5$$

Thus, the power of 10 representing this value is 5, making the order of magnitude 5.