Write the recurring decimal 0.4 as a fraction in its simplest form.

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CramX · Accepted Answer

Step 1: I'll solve this problem step by step, following the specified LaTeX formatting guidelines:. Step 2: : Set up the algebraic equation. Step 3: : Multiply the number by 10 to shift the decimal. Step 4: : Subtract the original equation from the multiplied equation. $-x = 0.4444...$ Step 5: : Solve for x. Step 6: : Verify the fraction. - 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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Step 1:
I'll solve this problem step by step, following the specified LaTeX formatting guidelines:

Step 2:
: Set up the algebraic equation

Step 3:
: Multiply the number by 10 to shift the decimal

Final Answer

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