Provide an Appropriate Response $.868686 \ldots$ To a Fraction by Writing It as the Infinite Series

question 345

Multiple Choice

Provide an appropriate response.
-Convert the decimal $.868686 \ldots$ to a fraction by writing it as the infinite series
$$\frac { 86 } { 100 } + \frac { 86 } { 100 ^ { 2 } } + \frac { 86 } { 100 ^ { 3 } } + \ldots$$

• A) \(0.87878788\)
• B) \(0.87\)
• C) \(\frac { 86 } { 99 }\)
• D) \(0.85\)

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Definitions:

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A sleep disorder characterized by pauses in breathing or instances of shallow or infrequent breathing during sleep.

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The process of taking air into and expelling it from the lungs to facilitate gas exchange with the internal environment, primarily by bringing in oxygen and flushing out carbon dioxide.

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The condition of suffering from a lack of sleep, which can affect cognitive functions, mood, and overall health.