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Which fractions are equivalent to 0.48‾0.4\overline{8}? Select all that apply.\newlineMulti-select Choices:\newline(A) 48100\frac{48}{100}\newline(B) 4899\frac{48}{99}\newline(C) 4490\frac{44}{90}\newline(D) 66135\frac{66}{135}

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Checkpoint: Rational and irrational numbersright chevron icon

Full solution

Q. Which fractions are equivalent to 0.48‾0.4\overline{8}? Select all that apply.\newlineMulti-select Choices:\newline(A) 48100\frac{48}{100}\newline(B) 4899\frac{48}{99}\newline(C) 4490\frac{44}{90}\newline(D) 66135\frac{66}{135}
  1. Convert to Fraction: Convert the repeating decimal 0.48‾0.4\overline{8} to a fraction. Let x=0.48‾x = 0.4\overline{8}. Then 10x=4.88‾10x = 4.8\overline{8}. Subtracting the original xx from this equation, 10x−x=4.88‾−0.48‾10x - x = 4.8\overline{8} - 0.4\overline{8}, results in 9x=4.49x = 4.4. Solving for xx gives x=4.49x = \frac{4.4}{9}.
  2. Simplify Fraction: Simplify the fraction 4.4/94.4/9. Since 4.44.4 can be written as 44/1044/10, the fraction becomes (44/10)/9=44/(10∗9)=44/90(44/10) / 9 = 44 / (10*9) = 44 / 90.
  3. Check Equivalency: Check if the simplified fraction 4490\frac{44}{90} is equivalent to any of the given choices. Simplify 4490\frac{44}{90} by dividing the numerator and denominator by their greatest common divisor, which is 22. This gives 4490=2245\frac{44}{90} = \frac{22}{45}, which is not listed in the choices.

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