Question

The circumference of Earth through the poles is 40,008 km. Round this number to four significant figures, and express it in standard exponential notation.

Answer 1

Significant figures rules

Perform operations as usual... then

account for the significant figures of each number.

Recall:

- ZEROS to the left do NOT matter ; 0.02 and 0.2 will have 1 sig. fig (digit = 2)

- ZEROS between numbers, DO matter 0.0202 and 0.202  will have 3 sig fig (digits 2, 0 and 2)

- ZEROS to the right, DO matter, since those show precise data i.e. 2.0 vs. 2.00 exists (2 sig fig. vs 3 sig. fig)

Then... apply rule, round as required

* Addition / Subscraction --> round answer to the LEAST sig. fig of the operation ( i.e. 2 sig fig vs. 3 sig fig --> round to 2 sig. fig)

* Multiplication/Division --> round answer to the LEAST sig. fig of the operation ( i.e. 2 sig fig vs. 3 sig fig --> round to 2 sig. fig)

4 sig fig --> 40008 --> 5 sig fig

4.0008*10^4

rouind to 5 sig fig

4.001*10^4 km