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Write the repeating decimal as a fraction.
Full solution
Q. Write the repeating decimal as a fraction.
- Denote Repeating Decimal as : Let's denote the repeating decimal as .
- Multiply by Power of : To convert this repeating decimal into a fraction, we can multiply by a power of that moves the repeating digits to the left of the decimal point. Since the repeating block is three digits long (), we multiply by (which is ).
- Subtract Original Number: Now, we subtract the original number from this new number to get rid of the repeating decimals.
- Perform Subtraction: Perform the subtraction on the left side of the equation:On the right side, the repeating decimals cancel out, leaving us with:So, we have:
- Solve for x: To solve for x, we divide both sides of the equation by :
- Simplify the Fraction: Now, we can simplify the fraction if possible. However, and do not have any common factors other than , so the fraction is already in its simplest form.
