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Q. Write the repeating decimal as a fraction.
- Rephrase Problem: Let's first rephrase the ＂How can the repeating decimal be expressed as a fraction?＂
- Identify Repeating Pattern: Identify the repeating pattern in the decimal. The digits ＂＂ repeat indefinitely, so we can write the decimal as
- Represent as Variable: Let's represent the repeating decimal as a variable, . So,
- Multiply by Power of : To convert the repeating decimal to a fraction, we can multiply by a power of that matches the length of the repeating pattern. Since ＂＂ has three digits, we multiply by (which is ). So,
- Subtract Decimal Parts: Now, subtract the original from to get rid of the decimal part. This gives us
- Perform Subtraction: Perform the subtraction: and . This gives us the equation .
- Divide by : To find the value of , divide both sides of the equation by . So, .
- Check for Simplification: Check if the fraction can be simplified. The numbers and do not have any common factors other than , so the fraction is already in its simplest form.
