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Write the repeating decimal as a fraction.
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Q. Write the repeating decimal as a fraction.
- Denote Repeating Decimal: Let's denote the repeating decimal by .To convert this repeating decimal into a fraction, we can use the following strategy: multiply by a power of that matches the length of the repeating sequence to shift the decimal point to the right, then subtract the original number from this result to eliminate the repeating part.
- Convert to Fraction: First, we identify the repeating sequence, which is . The length of this sequence is digits. Therefore, we multiply by (which is ) to shift the repeating sequence to the left of the decimal point.
- Multiply by Power of : Next, we subtract the original number from to get rid of the repeating decimal part.This simplifies to:
- Subtract Original Number: Now, we solve for by dividing both sides of the equation by .
- Solve for : We should 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.
