Convert 0.09¯¯¯¯¯
0.
09
¯
to a rational number in simplest form.(1 point)
To convert a repeating decimal to a rational number in simplest form, we let x= 0.09¯¯¯¯¯ and multiply both sides of the equation by 100:
100x = 9.99¯¯¯¯¯
x = 0.09¯¯¯¯¯
Next, we subtract the original equation from the new equation to eliminate the repeating part:
100x - x = 9.99¯¯¯¯¯ - 0.09¯¯¯¯¯
99x = 9.90
Finally, we divide both sides of the equation by 99 to solve for x:
99x/99 = 9.90/99
x = 0.1
Therefore, the rational number in simplest form that is equivalent to 0.09¯¯¯¯¯ is 0.1.