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

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To express 1.262626... as a quotient of whole numbers, it can be represented as a geometric series. The repeating decimal can be written as 1.26 + 0.00262626..., where the latter part can be expressed using the formula for a geometric series. This approach allows for the conversion of the repeating decimal into a fraction. Understanding geometric series is essential for this conversion, typically covered in calculus. The discussion emphasizes the importance of recognizing the properties of repeating decimals in mathematical expressions.
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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?
\sum_{n=0}^{\infty}x^n=\frac{1}{1-x}

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?
\sum_{n=0}^{\infty}x^n=\frac{1}{1-x}

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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