Write the repeating decimal as a fraction..009

To write the repeating decimal .009 as a fraction, we can follow these steps:

Step 1: Let x be the repeating decimal .009.

Step 2: Multiply both sides of the equation by 1000 (since there are three decimal places) to eliminate the decimal point: 1000x = 9.

Step 3: Subtract x from both sides of the equation: 1000x - x = 9 - .009.

Simplifying the equation gives us: 999x = 8.991.

Step 4: Divide both sides of the equation by 999 to solve for x: x = 8.991 / 999.

Step 5: Simplify the fraction 8.991 / 999 if possible. In this case, we can divide both the numerator and denominator by 9 to get x = 0.999 / 111.

Step 6: Simplify the fraction 0.999 / 111 further by dividing both the numerator and denominator by 0.999. This gives us x = 1 / 111.

Therefore, the repeating decimal .009 can be written as the fraction 1/111.