Numbers in Science

If there is originally exactly 1 mole of water (6.022 x 10²³ water molecules) in a beaker, and 1,000,000,000. evaporate every millisecond, how many water molecules are remaining after 7.00 days have elapsed?

Solution: All of them! Sketch:

To do this problem, you must figure out how many milliseconds there are in seven days, and then multiply this number times the number of atoms evaporating. Using the dimensional analysis setup shown below, we determine that we have lost 6.048 x 10¹⁷ atoms of water in seven days. If we subtract 6.048 x 10¹⁷ from 6.022 x 10²³, we get 6.022 x 10²³. At least to as many significant digits (3) as you have been given in the problem, the number of atoms would be reported the same. Does your calculator at least indicate some have evaporated? How many would have been left after the first day? The first second? What if you had tried to subtract the number per second -- second after second -- for the whole week? Would your calculator ever have shown a difference? Think about what you learned in the previous lesson about loss of significance.

Try another problem like this one.

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