Final answer:
To convert the repeating decimal 0.126126126... to a fraction in lowest terms, we can use the concept of geometric series. The fraction is 14/111.
Step-by-step explanation:
To convert the repeating decimal 0.126126126... to a fraction in lowest terms, we can use the concept of geometric series. Let's call the repeating block x. Then, multiplying x by 1000 gives us 1000x = 126.126126..., and subtracting x from 1000x gives us 999x = 126. Now, we can solve for x by dividing both sides by 999, which results in x = 126/999.
To simplify this fraction to lowest terms, we can divide both the numerator and denominator by their greatest common divisor, which is 9. So, 126/999 simplifies to 14/111.
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