Convert to a Fraction 0.8/0.11

Math
0.80.11
Create two equations where the only numbers to the right of the decimal place are the repeating part.
Set up an equation with 0.27‾.
x=0.27‾
Multiply both sides of x=0.27‾ by 100 to create the second equation.
100x=27.27‾
Subtract x=0.27‾ from 100x=27.27‾ to remove the repeating part.
99x=27
Divide each term by 99 and simplify.
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Divide each term in 99x=27 by 99.
99×99=2799
Cancel the common factor of 99.
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Cancel the common factor.
99×99=2799
Divide x by 1.
x=2799
x=2799
Cancel the common factor of 27 and 99.
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Factor 9 out of 27.
x=9(3)99
Cancel the common factors.
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Factor 9 out of 99.
x=9⋅39⋅11
Cancel the common factor.
x=9⋅39⋅11
Rewrite the expression.
x=311
x=311
x=311
x=311
Write as a mixed number by taking the whole number part along with the solution to the equation.
7311
Convert 7311 to an improper fraction.
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A mixed number is an addition of its whole and fractional parts.
7+311
Add 7 and 311.
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To write 7 as a fraction with a common denominator, multiply by 1111.
7⋅1111+311
Combine 7 and 1111.
7⋅1111+311
Combine the numerators over the common denominator.
7⋅11+311
Simplify the numerator.
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Multiply 7 by 11.
77+311
Add 77 and 3.
8011
8011
8011
8011
Convert to a Fraction 0.8/0.11

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