How do you convert 28.0 centimeters to meters with the correct number of significant figures? And how do you convert 1000 meters to kilometers with the correct number of significant figures?

The measurement 28.0 cm has three . To convert this to meters you need to divide 28.0 by 100 (because 1m = 100cm). The answer is 0.280 with the 0 at the far right being considered a significant figure because it comes to the right of the decimal point after non-zero digits.
I am assuming when you write 1000. meters you mean for the value to have four significant figures. To write this number with 4 sig figs it really should be written 1.000 x ##10^3##m. Some chem teachers would really frown on writing it as 1000. m to indicate four sig figs. (Did your teacher write it that way?)
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To convert from m to km you need to divide by 1000, so your answer will be 1. The correct way to write this to show 4 sig figs is: 1.000km