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Write the repeating decimal as a fraction.
Full solution
Q. Write the repeating decimal as a fraction.
- Identify repeating pattern: Question prompt: Write the repeating decimal as a fraction.
- Assign variable : Identify the repeating pattern in the decimal. The repeating pattern is .
- Shift decimal point: Let equal the repeating decimal, so
- Subtract original x: Multiply by to shift the decimal point three places to the right, aligning the repeating digits. This gives us
- Perform subtraction: Subtract the original from to eliminate the repeating decimals. This gives us
- Solve for x: Perform the subtraction: and . This results in the equation .
- Check fraction simplification: Solve for by dividing both sides of the equation by . This gives us .
- Check fraction simplification: Solve for by dividing both sides of the equation by . This gives us .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.
