Quandaries and Queries


Name: Erica

Who is asking: Student Level: Middle

To who ever is reading this email-

Yesterday in my 8th grade math class we were being taught how to convert a Repeating Decimal into a fraction. Since I, for some odd reason, seem to understand math better than the rest of my classmates, i began to drown out my teachers explaination for the rule. While she was about half way through with explaining mixed decimals i came up with an unsolvable question. Like I said before, I understand how to turn a repeating decimal into a fraction, but how would I turn a repeating .9 into a fraction? We all know it would equal 9/9, but doesn't 9 over 9 also equal 1? Even though it comes very close to one, it never really equals one. I'm very confused about this and i would love it if you could clear this up for me.




Hi Erica,

This does seem confusing. The procedure that your teacher showed you is probably the second method that Walter showed to Andrew when he asked this question. We received the same question from Catherine last year and Walter explained it again in slightly different words.

The number 0.999..., where the 9 repeats indefinitely, is another way of writing the number 1. If you read what Walter wrote maybe it will help explain why.


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