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Q. Write the repeating decimal as a fraction.
- Rephrase Problem: Let's first rephrase the problem into a single ＂How can the repeating decimal be expressed as a fraction?＂
- Identify Repeating Pattern: Identify the repeating pattern in the decimal. The digits ＂＂ repeat indefinitely, so we can write the decimal as
- Define Variable: Let be the repeating decimal, so
- Shift Decimal Point: Multiply by to shift the decimal point three places to the right, since the repeating pattern has three digits. This gives us
- Subtract Decimals: Now subtract the original from to eliminate the repeating decimals. This gives us
- Solve Equation: Perform the subtraction: and . This results in the equation .
- Divide by : Divide both sides of the equation by to solve for . This gives us .
- Simplify Fraction: Simplify the fraction by finding the greatest common divisor (GCD) of and . The GCD of and is , so the fraction is already in its simplest form.
- Final Result: Therefore, the repeating decimal can be expressed as the fraction .
