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 in 99x=27 by 99.

99×99=2799

Cancel the common factor of 99.

Cancel the common factor.

99×99=2799

Divide x by 1.

x=2799

x=2799

Cancel the common factor of 27 and 99.

Factor 9 out of 27.

x=9(3)99

Cancel the common factors.

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

A mixed number is an addition of its whole and fractional parts.

7+311

Add 7 and 311.

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.

Multiply 7 by 11.

77+311

Add 77 and 3.

8011

8011

8011

8011

Convert to a Fraction 0.8/0.11