Repeating decimal as infinite geometric series  Precalculus  Khan Academy  Summary and Q&A
TL;DR
The video explains how to represent a repeating decimal as an infinite geometric series and then expresses it as a fraction.
Questions & Answers
Q: How can a repeating decimal be represented as an infinite series?
A repeating decimal can be represented as an infinite series by considering the repeating pattern as individual terms in the series, with four zeroes before the decimal each time.
Q: Is the infinite series representing a repeating decimal a geometric series?
Yes, the infinite series representing a repeating decimal is a geometric series because the common ratio between each term is consistent. In this case, the common ratio is 10 to the negative fourth power.
Q: How can the sum of an infinite geometric series be expressed as a fraction?
The sum of an infinite geometric series can be expressed as a fraction using the formula a / (1  r), where "a" is the first term and "r" is the common ratio. In the case of the repeating decimal 0.4008, the fraction is 4,008 / 9,999.
Q: Can the fraction 4,008 / 9,999 be simplified?
Yes, the fraction 4,008 / 9,999 can be simplified by dividing both the numerator and denominator by 3. The simplified fraction is 1,336 / 3,333.
Summary & Key Takeaways

The video demonstrates how to represent a repeating decimal, such as 0.4008, as an infinite sum or series.

It shows that the repeating pattern 4008 can be viewed as individual terms in the series, with four zeroes before the decimal each time.

The video explains that this series is a geometric series with a common ratio of 10 to the negative fourth power.