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Write the repeating decimal as a fraction.
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Q. Write the repeating decimal as a fraction.
- Denote Decimal as : Let's denote the repeating decimal by the variable .
- Isolate Repeating Part: To convert the repeating decimal to a fraction, we first need to isolate the repeating part. We notice that the digits ＂＂ are repeating. To isolate this repeating part, we multiply by because there are three digits in the repeating sequence.
- Subtract and Solve: Now we subtract the original from to get rid of the decimal part. This will give us an equation with on both sides that we can solve for .
- Divide and Simplify: Now we solve for by dividing both sides of the equation by .
- Check Fraction: We should check if the fraction can be simplified. However, and do not have any common factors other than , so the fraction is already in its simplest form.
