Question

Convert 0.27¯¯¯¯¯
to a rational number in simplest form. (1 point)


A. 27/99


B. 12/7


C. 27/100


D. 3/11

Answer 1

wrong

Answer 2

To convert the repeating decimal 0.27¯¯¯¯¯ to a rational number, we can assign a variable to the repeating portion. Let x = 0.27¯¯¯¯¯.

To eliminate the repeating portion, we can multiply both sides of the equation by 100 to shift the decimal point two places to the right:
100x = 27.¯¯¯¯¯

Next, subtract the original equation from the shifted equation to eliminate the repeating portion:
100x - x = 27.¯¯¯¯¯ - 0.27¯¯¯¯¯
99x = 27

Now, divide both sides of the equation by 99 to solve for x:
x = 27/99

Therefore, the rational number in simplest form that is equivalent to 0.27¯¯¯¯¯ is 27/99.

The correct answer is A. 27/99.