MTH 151 – Mathematics for the Liberal Arts I
Numeration Application Directions

Purposes
This assignment will help you practice applying what you have learned about numeration systems to real problems or situations, and communicating about mathematical ideas with others.

Directions
Pick a problem:
Find a problem in your home, school, or work life, or in news reports of current events, that you can solve using what you learned about numeration in this unit.  If you work with computer hardware or software, you may need to use different number bases.  You might encounter the use of different scales of measurement and need to make conversions or interpretations of large numbers.  An astronomer, for example, thinks of distances in terms of light years, while chemists and computer chip engineers work in nanometers.   The national debt of the United States is so large that it’s almost unimaginable.  Could you explain it to a friend by using a different scale?
Solve the problem:
Use what you learned about numeration systems in this unit to solve your problem.  The better you use the appropriate mathematics to correctly solve the problem, the more points you will earn.
Present the problem and your solution to the others in the class:
Post a message in the application discussion forum for this unit.  In your message, describe the problem and how you solved it.  Use the equation editor as necessary to show the mathematical operations.  The better you communicate, the more points you will earn.  If you enjoy and know how to use multimedia, such as video, audio, and graphics, you may use those as well, but this is not required.
View and respond to the applications submitted by your classmates.
Pick two of your classmates’ applications that were particularly helpful to you.  Write a response to each, explaining in a paragraph or two why their applications helped you better understand the mathematics for this unit or better understand how the mathematics for this unit could be used outside of class.
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Example:  
The National US Debt is a number so big that the average person can't even fathom the amount. AT 11:30 a.m. April 6, the debt was fifteen trillion, five hundred seventy-nine billion, eight hundred fifty-two million, nine hundred forty-six thousand four hundred fifty-seven dollars or $15,579,852,946,457.
Computer programmers like using octal and hexadecimal because they are powers of 2 which computers use (binary). If I wanted to convert the debt decimal amount to hexadecimal, I would use the method of dividing by 16 and then using the remainders to create the hexadecimal number.
My hexadecimal representation of the US Debt is E2B6B64BC19.
I have to admit it doesn't look that bad using letters and numbers until you realize what the letters represent. To put the debt in more realistic terms for the average citizen to understand is that each citizen is in debt $49,871 and each tax payer is in debt $137,846. I'm not too happy about those numbers either.
OR
Statement of the problem
I wondered how many kings of France were named “Louis.”  On Wikipedia, I found a list of kings, from Louis I to Louis XIX.  http://en.wikipedia.org/wiki/King_Louis

For the first few names in the list, there could be more than one king with the same name. For this problem, I will ignore this complication and assume that there is one king of France for each name. However, the names are given in terms of Roman numerals. Thus, we must translate from Roman numerals to Hindu-Arabic numerals to find the number of kings.

Solution of the problem

The Roman symbol X represents 10 in Hindu-Arabic numerals, while I represents 1.  When a smaller value is to the left of a larger value, we subtract the smaller from the larger.
XIX = X + IX = 10 + 9 = 19.
Therefore, there are 19 kings of France named Louis.

Note that we cannot analyze this number as XI + X = (10+1) + 10 = 21, because we must write 20 as XX and then add I to get XXI.

Other Topics:  Roman numerals (Super Bowl, page numbering, determining age of buildings, etc.), binary/hexadecimal used in computing, size of solar system, cell size comparison, scientific notation

Grading Rubric:
Grading Criteria	Points Possible	
The problem:
•	Is it a real-life problem?
•	Is it challenging, not trivial?	5	
The strategies:
•	Are one or more general problem solving strategies used?
•	Are the strategies correctly identified?	5	
The presentation:
•	Is the problem explained well?
•	Are the problem solving strategies explained well?
•	Are the appropriate terms used?	3	
Your responses:
•	Did you post at least two responses?
•	Did you explain how the examples helped you better understand the math in this unit?
•	Did you ask questions for clarification or make suggestions on how to change or improve the original application posting or any other follow-up postings?	2