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Magazine Problem 9
Find a rational number that is bigger than 3.14159 but smaller than \(3.14159001\).
Problem 25
Show that the number 0 0100100010000100000100000010000000100 . . . . is irrational.
Problem 33
Suppose you are just a point and are standing on the number line at 1 but are dreaming of 0 . You take a step to the point \(1 / 2\), the midpoint between 0 and 1 . You proceed to move closer to 0 by taking a step that is half of the previous one. You continue this process again and again. Will you ever land on 0 ? Explain. Is this observation hard to accept?
Problem 39
Show that if a rational number has a decimal expansion that terminates (or alternatively, has a tail of zeros that goes on forever), then the rational number can be written as a fraction where the only prime numbers dividing the denominator are 2 and 5.
