Write the repeating decimal as a fraction..793893893…

To write the repeating decimal .793893893... as a fraction, we can follow these steps:

Step 1: Let x be the repeating decimal. x = .793893893...

Step 2: Multiply both sides of the equation by 1000 (since there are three digits repeating after the decimal point) to eliminate the repeating part. 1000x = 793.893893...

Step 3: Subtract the original equation from the equation obtained in step 2 to eliminate the repeating part. 1000x - x = 793.893893... - .793893893...

Simplifying the equation: 999x = 793

Step 4: Divide both sides of the equation by 999 to solve for x. x = 793/999

Step 5: Simplify the fraction if possible. The fraction 793/999 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 1. x = 793/999

Therefore, the repeating decimal .793893893... can be written as the fraction 793/999.