Solving for 100x: A Math Puzzle

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Homework Help Overview

The discussion revolves around converting a repeating decimal into a fractional form, specifically focusing on the example of x = 0.91919191. Participants are exploring the mathematical technique used for this conversion and its implications.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the method of multiplying the decimal by 100 to facilitate the conversion to a fraction. Some express curiosity about the appropriate contexts for using this technique, while others emphasize its role in demonstrating the nature of periodic decimals as rational numbers.

Discussion Status

The conversation is active, with various interpretations of the technique being explored. Some participants provide insights into its purpose, while others question the framing of its usage. There is no explicit consensus, but productive dialogue is ongoing regarding the mathematical principles involved.

Contextual Notes

Participants note the challenge of finding references in textbooks related to this technique, indicating a potential gap in available resources or explanations on the topic.

thomas49th
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Hi, I recall a thingy when you have somthing like

x = 0.91919191

then you go 100x = 91.919191
100x - x = 91

When do you use this? It's in conjuction with somthing else... looked in my textbook can't find it.

Thanks
 
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Personally, I use that when I have a repeating, non-terminating decimal that I want to get in fractional form so it looks prettier in an equation.
 
Why should you care "when is it used"?
It is a wrong question; the technique is never "used"; rather, it illustrates how you may rewrite a periodic decimal as a fraction.

That is, the technique amounts to a constructive PROOF of a certain mathematical proposition:
namely that any periodic decimal can be written as a fraction between two natural numbers, i.e a periodic decimal is necessarily a rational number.
 
100x - x=99x=91

x=91/99

Thats why its used, to get urself a fraction.
 

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