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Write the repeating decimal as a fraction.
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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 repeating pattern is , which means the decimal can be written as
- Represent as Variable: Let's represent the repeating decimal as a variable, say . So, let
- Isolate Repeating Part: To isolate the repeating part, we can multiply by , because the repeating part is three digits long. This gives us
- Subtract Decimals: Now, subtract the original from to get rid of the decimal part. This gives us
- Solve for x: Perform the subtraction: . This is because the repeating decimals cancel each other out.
- Simplify Fraction: Now, solve for by dividing both sides of the equation by . This gives us .
- Final Fraction: To simplify the fraction, we look for the greatest common divisor (GCD) of and . The GCD of and is , so the fraction is already in its simplest form.
- Final Fraction: To simplify the fraction, we look for the greatest common divisor (GCD) of and . The GCD of and is , so the fraction is already in its simplest form.Therefore, the repeating decimal as a fraction is .
