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Write the repeating decimal as a fraction.
Full solution
Q. Write the repeating decimal as a fraction.
- Identify Repeating Part: Let's identify the repeating part of the decimal. The digits repeat indefinitely, so we can express the decimal as
- Represent as : Let's represent the repeating decimal as :
- Isolate Repeating Part: To isolate the repeating part, we can multiply by , since the repeating part is three digits long:
- Subtract Original : Now, we subtract the original from to get rid of the decimal part:
- Perform Subtraction: Perform the subtraction:
- Solve for x: Now, we solve for by dividing both sides of the equation by :
- Check Fraction Simplification: We can check if the fraction can be simplified. The numerator and denominator do not have any common factors other than , so the fraction is already in its simplest form.
