Probably the movement on a swing can be approximated by assuming that the magnitude of each swing will be a certain percentage of the previous swing (because of lost energy).
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The ball does not return to its initial height after bouncing. So the height it reaches after the first bounce will be a fraction of the initial height, etc. This is a geometric sequence with common ratio 5/8.
"Not as a decimal or fraction as there are an infinite number of digits." This is a common and useful answer. The *correct* answer is that PI is firstly an irrational number that cannot be calculated from any ratio (fraction). Secondly, PI is a transcendental number that, by the definition of "transcendental", cannot be exactly calculated. The nest you can do is to apply an infinite convergent series that becomes more and more accurate with more and more decimal places.
A set of numbers is bounded if there exist two numbers x and y (with x ≤ y)such that for every member of the set, x ≤ a ≤ y. A set is unbounded if one or both of x and y is infinite. Similar definitions apply for sets in more than 1 dimension.
yes. technically all decimals have an infinite amount of zeros behind them. you just have to apply significant digits to find how much zeros you are suppose to write.