The Number Devil
Fourth Night
Due: December 19th
Answer the following questions in essay form. Use the information given to guide your responses. Be sure to show the responses to each part even if it is a mathematical answer.
Start your essay with an introduction. What are the main points? Talk about one or two main points briefly.
® Convert the following fractions to decimal form.
1 2 3 4 5
5 5 5 5 5
1 2 3 4 5 6
6 6 6 6 6 6
® Does the numerator or the denominator have a greater effect on determining whether the decimal form of the fraction will be repeating or terminating? Why do you think this is the case?
® Using a calculator, determine if the following terminate or repeat when in decimal form:
1 1 1 1 3 1 11 2 4 5 1 1 6
128 8 16 45 10 100 1000 5 13 12 7 55 11
® Choose ten of your own fractions (you can make them up) and predict whether they will terminate or repeat. Make sure to use reasonable numbers (numbers that aren’t too big) and a good variety of fractions. Don’t just choose similar numbers! (like 1/7, 2/7, 3/7, etc)
® Explain how you made your predictions.
® Find the prime factorization of the denominators of each of your fractions. What do you notice about the prime factorization of those denominators of fractions that terminate and those that repeat?
® Write a rule to describe how you can tell just by looking at a fraction that the number will repeat or terminate in decimal form.
End your essay with a conclusion. Briefly summarize a FEW main points. You do not have to restate everything you already talked about!
