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Write the repeating decimal as a fraction.
Full solution
Q. Write the repeating decimal as a fraction.
- Rephrase Problem: Let's first rephrase the problem as a ＂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
- Assign Variable: Let equal the repeating decimal, so
- Shift Decimal Point: Multiply by to shift the decimal point three places to the right, since there are three repeating digits. This gives us
- Subtract Decimals: Subtract the original from to get rid of the repeating decimals. This gives us
- Perform Subtraction: Perform the subtraction: and . This results in the equation .
- Solve for x: Solve for x by dividing both sides of the equation by . This gives us .
- Check Fraction 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.
