Critical thinking and number sense based math problems to challenge students of all grade levels. Most of these problems require more critical thinking and less number crunching than typical textbook math problems. Check back 5 days per week for a new problem.
Some students will know the procedure for converting repeating decimals to fractions. They can simply convert .9999.... into a fraction and reduce 9/9 to 1.
Other students can approach it from the concept of a limit. Try asking the question "what is .99999... really close to" - to which the student will reply 1. Then ask "are there any number between .9 repeating and 1?". Since there are no number between .9 repeating and 1, they must be the same thing.
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Solutions:
Some students will know the procedure for converting repeating decimals to fractions. They can simply convert .9999.... into a fraction and reduce 9/9 to 1.
Other students can approach it from the concept of a limit. Try asking the question "what is .99999... really close to" - to which the student will reply 1. Then ask "are there any number between .9 repeating and 1?". Since there are no number between .9 repeating and 1, they must be the same thing.
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