Rounded to the nearest hundredth, numbers look like this:
[tex]\ldots 0.60,\ 0.61,\ 0.62,\ 0.63,\ldots[/tex]
So, our number lies between 0.62 and 0.63. We have to check which of the two is closer. To measure the distance between numbers, we use the absolute value of the difference:
[tex]|0.6288-0.62|=0.0088,\quad |0.6288-0.63|=0.0012[/tex]
Since [tex]0.0012<0.0088[/tex], we deduce that 0.63 is closer to 0.6288 than 0.62, and thus it's a better approximation.
