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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:
- Set Variable : Let equal the repeating decimal with repeating (). We will use this variable to represent the repeating decimal and solve for it as a fraction.
- Isolate Repeating Part: To isolate the repeating part, we multiply by , since there is one digit before the repeating pattern. This gives us .
- Multiply by : Next, we multiply by , since there are two digits in the repeating pattern (). This gives us .
- Subtract Equations: Now we have two equations: and . We will subtract the first equation from the second to eliminate the repeating decimals. This gives us
- Divide by : Performing the subtraction, we get . This is because the repeating decimals cancel each other out.
- Check for Simplification: To find the value of , we divide both sides of the equation by . So, .
- Check for Simplification: To find the value of , we divide both sides of the equation by . So, .We check if the fraction can be simplified further. Since is a prime number and does not share any common factors with other than , the fraction is already in its simplest form.
