QQuestionMathematics
QuestionMathematics
Write the decimal 0.27 repeated as a fraction in simplest form.
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Answer
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Step 1:I'll solve this step-by-step using the specified LaTeX formatting guidelines:
Step 2:: Understand the Notation
The decimal 0.27 repeated means the digits 27 repeat infinitely: 0.272727...
Step 3:: Set Up the Algebraic Equation
Let $$x = 0.272727...
Step 4:: Multiply Both Sides by 100
100x = 27.2727...
Step 5:: Subtract Original Equation from Multiplied Equation
99x = 27
x = 0.2727...
Step 6:: Solve for x
x = \frac{27}{99}
Step 7:: Simplify the Fraction
\frac{27}{99} = \frac{3}{11}$$ (by dividing both numerator and denominator by their greatest common factor of 9)
Final Answer
\frac{3}{11}
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