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Write the repeating decimal as a fraction.
Full solution
Q. Write the repeating decimal as a fraction.
- Rephrase the Problem: Let's first rephrase the ＂Convert the repeating decimal to a fraction.＂
- Identify Repeating Pattern: Identify the repeating pattern in the decimal. The pattern is which repeats indefinitely.
- Define Variable: Let be the repeating decimal, so
- Shift Decimal Point: Multiply by to shift the decimal point three places to the right, aligning the repeating digits. This gives us
- Subtract Decimals: Subtract the original from to eliminate the repeating decimals. This gives us
- Simplify Equation: Perform the subtraction: . This simplifies to .
- Divide to Solve: Divide both sides of the equation by to solve for . This gives us .
- Check for Simplification: Check if the fraction can be simplified. The numbers and do not have any common factors other than , so the fraction is already in its simplest form.
