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From Euclid to Spigotry
Assignment 20 (outline 16) 
Last modified: September 15, 2004
1. Find a fraction a/b, in lowest terms, for which a/b = 0.980198019801....
(This problem appeared in the American AIrlines inflight magazine for August 2003)
2. A well-known irrational number has a hexadecimal representation that starts 1.6A09E66.
Using the Windows scientific calculator, find the first three digits after the decimal point when the number is expressed in decimal notation, and guess what the number is. You can confirm your guess by multiplying the number by 167 (to make it an integer) and squaring. 

3. Continue the process begun in class (lecture topic 6) to get approximations for 10000p and 100000p, each as the sum of a base 10 integer and a base 16 fraction.  Use the Windows scientific calculator in hexadecimal mode.
4. In the mixed-radix notation used for the spigot algorithm, p/2 = 1.1111111....
i.e p/2 =  
Start with 1.111 and use the spigot algorithm to find the first two digits after the decimal point. You will not get more than one digit of p/2 after the decimal point correct, since