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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 algebra to create an equation that we can solve for .
- Multiply by : First, we multiply by to shift the decimal two places to the right, since the repeating pattern is two digits long.This step ensures that when we subtract from , the decimal parts will align and the repeating parts will cancel out.
- Subtract to Eliminate Repeating Decimal: Now, we subtract the original from to get rid of the repeating decimal part.We are left with a simple equation without the repeating decimal.
- Solve for x: Next, we solve for by dividing both sides of the equation by .This gives us the fraction form of the repeating decimal.
- Check for Simplification: Finally, we check if the fraction can be simplified. However, since and have no common factors other than , the fraction is already in its simplest form.
