Converting the number 2.3171717... into the fraction 1147/495 via the Geometric Series

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In this video, I go over an example of converting the number 2.3171717... (with infinite repeating 17) into a fraction by writing the repeating 17s as an infinite geometric series with common ratio 1/100, hence the sum is convergent. Thus, we can use the formula for the sum of a geometric series, and a bit of algebra, to obtain the fraction of integers 1147/495. This is a great example illustrating the powerful tool that the geometric series is in simplifying a number made up of repeating digits.

#math #calculus #series #geometricseries #education

Timestamps

• Example 3: Write the number 2.3171717... as the ratio of integers – 0:00
• Solution: Separating the number into a convergent geometric series with common ratio 1/100 (which is less than 1) – 0:11
• Using the formula for the sum of a geometric series to obtain our number as a fraction – 2:49
• Solving 23 * 99 = 2294 by hand – 5:44
• After a lot of manual algebra, we get 1147 / 495 – 8:40

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