Decimal Squares Model The Investigation below poses questions to generate interest in various mathematical topics from the text and encourages students to formulate and investigate their own conjectures. One use of the investigations is for term papers in which students report on their conjectures and the patterns they find. Click on the Read Me file below to open the investigation in a Word file: Read Me - Repeating Decimals Instructions (Word Format) (23.0K) The Math Investigator is a data collection software program that may be used to collect data for the investigation. You may type answers onto the Word file or copy and paste in data from the Investigator. Click here to launch the Repeating Decimals InvestigatorMath Investigator 6.1REPEATING DECIMALS on the Math Investigator prints decimals for rational numbers. If the decimal is repeating, it counts the number of digits in the nonrepeating part (if any) and the number of digits in the repetend. Starting Points for Investigations
a. What type of fractions have terminating decimals? Form a conjecture and test it for other fractions. b. Form a conjecture about the type of fractions which have repeating decimals with a nonrepeating part. For example, 1/12 = .08333 . . . has two digits before the repetend which is repeating 3s. Is there a pattern for predicting the number of digits in the nonrepeating part of a decimal? c. If a repeating decimal does not have a nonrepeating part, it is called purely periodic. For example, 1/7 = .142857 . . . is purely periodic. What types of fractions will have decimals that are purely periodic? d. The number of digits in the repetend of the decimals for some of these fractions is one less than the denominator. For example, the repetend for 1/17 has 16 digits. For what types of numbers n will the repetend for 1/n have n - 1 digits? | ||||||
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