QQuestionMathematics
QuestionMathematics
Write the recurring decimal 0.4 as a fraction in its simplest form.
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Answer
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Step 1:I'll solve this problem step by step, following the specified LaTeX formatting guidelines:
Step 2:: Set up the algebraic equation
Let $$x = 0.4444...$$ be the recurring decimal
Step 3:: Multiply the number by 10 to shift the decimal
10x = 4.4444...
Step 4:: Subtract the original equation from the multiplied equation
9x = 4
-x = 0.4444...
Step 5:: Solve for x
x = \frac{4}{9}
Step 6:: Verify the fraction
- The fraction $$\frac{4}{9}$$ is already in its simplest form
- No further reduction is possible
Final Answer
Key Insights: - This method works by creating an algebraic equation that eliminates the repeating decimal - The process involves multiplying by a power of 10 and subtracting to isolate the variable - The resulting fraction \frac{4}{9} is equivalent to the original recurring decimal 0.4
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