Convert 0.27¯¯¯¯¯
to a rational number in simplest form.(1 point)
Responses
27/100
27/99
3/11
1/27
The correct answer is: 27/100
To convert the repeating decimal 0.27¯¯¯¯¯ to a rational number in simplest form, we can represent it as a fraction.
Let x = 0.27¯¯¯¯¯
Multiplying both sides of the equation by 100, we get:
100x = 27.27¯¯¯¯¯
Subtracting the original equation from the equation above, we get:
100x - x = 27.27¯¯¯¯¯ - 0.27¯¯¯¯¯
99x = 27
Dividing both sides of the equation by 99, we get:
x = 27/99
Therefore, the rational number in simplest form that represents 0.27¯¯¯¯¯ is 27/99.