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Convert the following repeating decimal to a fraction in simplest form. .0 bar(4) Answer:

Convert the following repeating decimal to a fraction in simplest form.\newline.04‾ .0 \overline{4} \newlineAnswer:

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Full solution

Q. Convert the following repeating decimal to a fraction in simplest form.\newline.04‾ .0 \overline{4} \newlineAnswer:
  1. Assign Variable xx: Let xx equal the repeating decimal 0.44‾0.4\overline{4}.\newlinex=0.44‾x = 0.4\overline{4}
  2. Convert to Fraction: To convert the repeating decimal to a fraction, we can set up an equation where the repeating part is isolated on one side. Since there is one digit repeating, we multiply xx by 1010 to shift the decimal point one place to the right.\newline10x=4.44‾10x = 4.4\overline{4}
  3. Subtract Equations: Now we have two equations:\newline11. x=0.4‾x = 0.\overline{4}\newline22. 10x=4.4‾10x = 4.\overline{4}\newlineSubtract the first equation from the second to eliminate the repeating decimal.\newline10x−x=4.4‾−0.4‾10x - x = 4.\overline{4} - 0.\overline{4}
  4. Perform Subtraction: Perform the subtraction: 9x=49x = 4
  5. Solve for x: Now, solve for x by dividing both sides of the equation by 99. \newlinex=49x = \frac{4}{9}
  6. Fraction in Simplest Form: The fraction 49\frac{4}{9} is already in its simplest form, as 44 and 99 have no common factors other than 11.

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