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Convert the following repeating decimal to a fraction in simplest form.Answer:
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Q. Convert the following repeating decimal to a fraction in simplest form.Answer:
- Define as repeating decimal: Let equal the repeating decimal We will multiply by a power of that will move the decimal point to the right so that the same digits are aligned after the decimal point.
- Multiply by : Since the repeating pattern is two digits long, we will multiply by to shift the repeating digits to the right of the decimal point.Now we have a new equation where the decimal part of is the same as the decimal part of .
- Subtract original equation: Next, we will subtract the original equation from the new equation to eliminate the repeating decimals.
- Solve for x: Now we solve for by dividing both sides of the equation by .
- Check for simplification: We check to see if the fraction can be simplified further. Since and have no common factors other than , the fraction is already in its simplest form.
