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Write the repeating decimal as a fraction.
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Q. Write the repeating decimal as a fraction.
- Identify Repeating Decimal: Let's identify the repeating part of the decimal. The digits repeat indefinitely, so we can express the repeating decimal as
- Set Decimal as Variable: To convert this repeating decimal to a fraction, we can set it equal to a variable, let's say :
- Isolate Repeating Part: To isolate the repeating part, we can multiply by , since there are three digits in the repeating sequence:
- Subtract and Simplify: Now, we subtract the original from to get rid of the decimal part:This simplifies to:
- Divide to Find x: To find the value of x, we divide both sides of the equation by :
- Simplify Fraction: We can simplify the fraction by looking for common factors between the numerator and the denominator. In this case, there are no common factors other than , so the fraction is already in its simplest form.
