Final answer:
To convert 0.00888888... into a reduced fraction, multiply the equation by 10000 and subtract the original equation to obtain a fraction. Continuing to reduce the fraction, divide both the numerator and denominator by the greatest common divisor (GCD). The reduced fraction is 11.111... divided by 1250.
Step-by-step explanation:
To convert 0.00888888... into a reduced fraction, we can represent it as an equation:
x = 0.00888888...
Multiplying both sides of the equation by 10000 to eliminate the decimal places, we get:
10000x = 88.88888...
Subtracting the original equation from this new equation, we get:
9999x = 88.88...
Now, we can express the decimal as a fraction by dividing both sides of the equation by 9999:
x = \frac{88.88...}{9999}
To further reduce the fraction, we can divide the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD is 8, so:
x = \frac{11.111...}{1250}
Therefore, the reduced fraction for 0.00888888... is \frac{11.111...}{1250}.
Learn more about Converting repeating decimals to fractions