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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:
- Write as decimal: Let equal the repeating decimal with repeating. We can write this as:
- Multiply by : To convert the repeating decimal to a fraction, we can create an equation that isolates the repeating part. Multiply by , since there are two digits in the repeating sequence, to shift the decimal two places to the right:
- Subtract from : Now, subtract the original from to get rid of the repeating part:This simplifies to:
- Divide by : To find the value of , divide both sides of the equation by :
- Check for simplification: Now, we need to check if the fraction can be simplified. The numbers and have no common factors other than , so the fraction is already in its simplest form.
