Is a Fraction a Repeating or Terminating Decimal? submitted by: Jeff LeMieux, May 2003 This narrative describes how I use my javascript tool, cataloged in the Math Tools digital library, in the classroom. Course: Math 7 Topic: Relations of Common and Decimal Fractions Resource type: JavaScript Resource location: http://www2.whidbey.net/ohmsmath/webwork/javascript/denom.html Math Forum catalogue entry: http://mathforum.org/mathtools/tool.html?rc=tool&new_id=800 Story:   This JavaScript was the direct result of students trying to determine if fractions resulted in terminating or repeating decimals while using scientific calculators. While more common fractions were relatively simple to determine, there were instances where the propensity of the calculator to round the last digit gave students false data. Similarly, the limit to the number of digits displayed created another difficulty. Various computer languages also limit the number of places available for solutions. Since the output is available in a text window, it can be manipulated in the window or cut and pasted into another application so that the repeating pattern can be determined and aligned. 0.001949317738791 42300194931773879 14230019493177387 91423001949317738 79142300194931773 87914230019493177 38791423001949317 0.001949317738791423 001949317738791423 001949317738791423 001949317738791423 001949317738791423 001949317738791423 etc. Other questions generated were: What kind of numbers generate terminating decimals? What kind of denominators generate repeating decimals? What effect does the numerator have on the repeating decimal portion? How long a sequence is generated before the pattern repeats? Is there a maximum length for the pattern before it repeats? Can the length of the sequence be predicted? Which Prime Numbers do not generate a repeating sequence? Where and how I used this: This script was originally used as a follow-up activity to an exercise on changing repeating decimals to fractions. It was designed to answer the question how you would know if a fraction became repeating or terminating given the limitations of calculators and the difficulties of long-hand solutions. It later served as an adjunct to lessons on rational/irrrational numbers. Originally it appeared as an insert to the on-line lesson plans during the week it was covered. Send comments to Jeff LeMieux at tackweed@whidbey.net Jeff LeMieux May 2003 http://www2.whidbey.net/ohmsmath