PROBLEM 1 (due Oct 19, 10 points)


We want to find to within a factor of 2 the largest positive number that can be represented in Excel.

Remark: A number is within a factor of 2 of the right answer if it lies any where between one half of the right answer and twice the answer, exclusively. For example, if the right answer is 18, then any number strictly larger than 9 but strictly less than 36 will be acceptable.

A most straightforward way is to first enter the number 1 in cell A1. Then in cell A2 enter the formula =2*A1 and you should see the displayed value of 2 in cell A2. Next copy that formula. Highlight cells A3 to A? where ? represents a large positive number at least over a few hundreds of even a few thousands. You need to experiment to see how large it has to be. Paste that formula in those cells (remember how to do that). You will see that the values in each successive cell doubles until the number becomes so large that Excel can no longer represent.
Now put in column C the following results:

  1. What is displayed in the cell when that happens?
  2. What is displayed in the cells that follow?
  3. What is the largest value that you see displayed? This number must be within a factor of 2 the largest number that can be represented.
  4. That value can be found in which row?