Convert 0.27¯¯¯¯¯
to a rational number in simplest form.(1 point)
Responses
27100
Start Fraction 27 over 100 end fraction
2799
Start Fraction 27 over 99 end fraction
127
Start Fraction 1 over 27 end fraction
311
Start Fraction 27 over 100 end fraction
To convert 0.27¯¯¯¯¯ to a rational number in simplest form, we can write it as a fraction. Let's represent the repeating decimal as "x" and set up an equation to solve for "x".
x = 0.27¯¯¯¯¯
Multiply both sides of the equation by 100 (to move the decimal point to the right):
100x = 27.¯¯¯¯¯
Subtract the original equation from this equation:
100x - x = 27.¯¯¯¯¯ - 0.27¯¯¯¯¯
99x = 27
Divide both sides of the equation by 99 to solve for "x":
x = 27/99
Therefore, 0.27¯¯¯¯¯ can be written as the rational number "27/99" in simplest form.