Final answer:
To write 0.126126126 as a fraction in lowest terms, we can first convert the repeating decimal to a fraction over 9s and then simplify it to its lowest terms.
Step-by-step explanation:
To write 0.126126126 as a fraction in lowest terms, we need to convert the repeating decimal 0.126 into a fraction. To do this, we'll use the fact that the repeating decimal can be represented as a fraction over 9s:
Let x = 0.126126126...
Then, multiplying both sides by 1000, we get 1000x = 126.126126126...
Now, subtracting the original equation from this new equation, we get 999x = 126.126 - 0.126
Simplifying, we have 999x = 126
Dividing both sides by 999, we find x = 126/999
This fraction can be simplified further by dividing the numerator and the denominator by their greatest common divisor, which is 9. Therefore, the fraction in lowest terms is 14/111.
Learn more about Converting Repeating Decimals to Fractions