Converting 1.262626... to a Quotient of Whole Numbers: Tricks to Solve

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SUMMARY

The discussion centers on converting the repeating decimal 1.262626... into a quotient of whole numbers. The correct approach involves recognizing 1.262626... as a geometric series, specifically expressed as 1 + 0.262626..., where 0.262626... can be represented using the formula for a geometric series. The final result is that 1.262626... equals 1 + (26/99), leading to the quotient of 128/99. This method is essential for accurately converting repeating decimals into fractions.

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  • Learn how to convert repeating decimals to fractions
  • Explore the concept of limits in calculus
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abbeyofthelema
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i am being asked to express 1.262626... as a quotient of two whole numbers. would the answer to this be a simple 1.262626.../1000000?
I know I am doing something wrong, but I am not sure what.
 
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1.262626... is not a whole number.

Are you familiar with the geometric series?
[tex]\sum_{n=0}^{\infty}x^n=\frac{1}{1-x}[/tex]

Can you write 1.262626... as a geometric series?
 
Galileo said:
1.262626... is not a whole number.

Are you familiar with the geometric series?
[tex]\sum_{n=0}^{\infty}x^n=\frac{1}{1-x}[/tex]

Can you write 1.262626... as a geometric series?
I just have to say that is so cool. Eh, you would learn that in calculus, right?
 

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