Let \( x = 0.5\overline{5} \).
This means that \( x = 0.55555...\)
To convert this repeating decimal into a fraction, we can use the following steps:
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Multiply \( x \) by 10 to shift the decimal point one place to the right:
\[ 10x = 5.55555... \]
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Now, we have two equations: \[ x = 0.55555... \] \[ 10x = 5.55555... \]
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Next, we subtract the first equation from the second:
\[ 10x - x = 5.55555... - 0.55555... \] \[ 9x = 5 \]
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Now, divide both sides by 9:
\[ x = \frac{5}{9} \]
Therefore, \( 0.5\overline{5} \) as a fraction is \( \frac{5}{9} \).
The correct response is:
Start Fraction 5 over 9 End Fraction
1 answer