Convert 0.09¯¯¯¯¯
to a rational number in simplest form.(1 point)
0.09¯ can be expressed as the fraction 1/11.
To convert the repeating decimal 0.09¯¯¯¯¯ into a rational number in simplest form, we can use a few steps:
Step 1: Let x = 0.09¯¯¯¯¯
Step 2: Multiply both sides of the equation by 100 to eliminate the repeating decimal:
100x = 9.999¯¯¯¯
Step 3: Subtract the original equation from the multiplied equation to eliminate the repeating decimal:
100x - x = 9.999¯¯¯¯ - 0.09¯¯¯¯¯
99x = 9.909¯¯¯¯¯
Step 4: Now, subtract 9 from both sides to isolate the repeating decimal:
99x - 9 = 9.909¯¯¯¯¯ - 9
99x - 9 = 9.819¯¯¯¯¯
Step 5: Simplify the equation by dividing both sides by 99:
(99x - 9) / 99 = 9.819¯¯¯¯¯ / 99
x - 0.09 = 0.099¯¯¯¯
Step 6: Add 0.09 to both sides of the equation to solve for x:
x - 0.09 + 0.09 = 0.099¯¯¯¯ + 0.09
x = 0.189¯¯¯¯¯
Therefore, the repeating decimal 0.09¯¯¯¯¯ can be written as the rational number 0.189¯¯¯¯¯ in simplest form.
To convert 0.09¯¯¯¯¯ to a rational number in simplest form, we can set x = 0.09¯¯¯¯¯ and subtract it from 100x:
100x - x = 9.09¯¯¯¯¯ - 0.09¯¯¯¯¯
99x = 9
x = 9/99
Therefore, 0.09¯¯¯¯¯ in simplest form as a rational number is 9/99.