Calculus 2: Infinite Sequences and Series (38 of 62) The Geometric Series: Example 2

In this video I will find the fractional equivalence of a repeating decimal number.

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[georgeninan]

# there is another method: set x=2.71828, 1828, 1828...; multiply both sides by 10, 000; subtract the second equation from the first; now we have 9, 999x = 27180.1 as the 1828s would have lined up and would cancel out; solve for x. this gives 271801/99990. the algorithm used is that as the repeating digits commence 5 digits right of the decimal use 10, 000 to create the second equation. much quicker, and less complicated too