```Date: Oct 24, 2012 2:27 PM
Author: Teague, Dan
Subject: RE: [ap-calculus] e and "lies my calculator tells me."

NOTE: This ap-calculus EDG will be closing in the next few weeks. Please sign up for the new AP CalculusTeacher Community Forum at https://apcommunity.collegeboard.org/getting-startedand post messages there. ------------------------------------------------------------------------------------------------Erin,To follow up on Doug's nice example and explanation, your students might be interested in the following experiment.In their favorite language and on their favorite computer, write the following program:H = 1/2X=2/3 - HY = 3/5 - HE = (X+X+X) - HF = (Y+Y+Y+Y+Y) - HQ = F/EPrint QSince the computer is working in base 2, there are five possible values for Q.  For me, Q = 2, but other machines using others lengths of representations and using a processor that rounds or truncates can produce values of Q equal to 1, -1 , -2, 2, 4, and 1.5.Since my machine gives me I know that my machine uses a number of digits that is a multiple of 4 and rounds off at the end.If you get 4, then your machine is using a number of digits that are 3 more than a multiple of 4 and truncates at the end.To see this, have them write out the binary representation using 5, 6, 7, or 8 digits and truncating or rounding at the end.  Then just do the addition and subtraction.H = 0.1      X = 0.001010101010...     Y = 0.000110011001100...For example, with 6 digits with rounding, we have:H = 0.1X = 0.001011    so   X+X+X = 0.100001 and E = 0.000001Y = 0.000110    so   Y+Y+Y+Y+Y = 0.011110 and F = -0.000010So Q = F/E = -2.DanDaniel J. TeagueDepartment of MathematicsNC School of Science and Mathematics1219 Broad StreetDurham, NC 27705teague@ncssm.edu---To search the list archives for previous posts go tohttp://lyris.collegeboard.com/read/?forum=ap-calculus
```