Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Session 7:
Homework

Problem H1

 a. Find the fractional equivalent for 0.142857. b. Find the fractional equivalent for 0.142857142857142857....

 Problem H2 Shigeto and Consuela were computing the decimal expansion of 1/19. Since Shigeto used scratch paper, he had only a little room to write his answer. He continued writing the digits on the next line, and in the end, his answer looked like this: Shigeto noticed a pattern in these numbers. Describe his pattern.

 Look at the columns of digits. What do you notice?   Close Tip Look at the columns of digits. What do you notice?

 Problem H3 Consuela did her computation on a narrow notepad. Her answer looked like this: After looking at Shigeto's pattern, Consuela tried to find a pattern in her answer. What observations can you make about Consuela's pattern?

 Look at the columns of digits. What do you notice?    Close Tip Look at the columns of digits. What do you notice?

 Problem H4 David started to compute the decimal expansion of 1/47. He got tired after computing this much of the expansion: Shigeto had no trouble finishing the expansion using his pattern. How about you? Can you finish the expansion and explain your answer?

 What are the possible periods for the decimal expansion of 1/47? Can you predict the actual period based on how many digits there are in the decimal expansion so far? How would you arrange those digits so that the columns add up to 9?    Close Tip What are the possible periods for the decimal expansion of 1/47? Can you predict the actual period based on how many digits there are in the decimal expansion so far? How would you arrange those digits so that the columns add up to 9?

 Problem H5 Does the length of the period of your expansion make sense? Explain why or why not.

 Problem H6 Consuela looked at David's work and knew immediately that her method would not be helpful. Explain why not.

 Problem H7 Mr. Teague asked the class to compute a decimal expansion with period 42. Unfortunately, his dog spilled paint on Shigeto's and Consuela's answers. Use the visible information in Shigeto's and Consuela's answers and the patterns you have seen to find the complete decimal expansion:

 Problem H8 Find the fraction with this particular decimal expansion.

 Problem H9 Is it possible to represent the number 1 as a repeating decimal?

 Think about the decimal expansion for 1/3 = 0.333333.... What would 2/3 be? What fraction would be closest or equal to 1?   Close Tip Think about the decimal expansion for 1/3 = 0.333333.... What would 2/3 be? What fraction would be closest or equal to 1?

 Problem H10 Is it possible to predict the period of 1/14 if you know the period of 1/7 (i.e., six)?

 Problem H11 Is it possible to provide a convincing argument to prove that the decimal expansion of 1/n has a period that is less than n?

 Problems H2-H11 adapted from Findell, Carol, ed. Teaching with Student Math Notes, Volume 3. p. 121. © 2000 by the National Council of Teachers of Mathematics. Used with permission. All rights reserved.
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