write 076 repeated indefinitely as a fraction

Answer 1

To express the decimal number 0.076 repeated indefinitely as a fraction, we can use the following steps:

Step 1: Let x be the number we want to express as a fraction. In this case, x = 0.076.

Step 2: Multiply both sides of the equation by 1000 to move the decimal point three places to the right:
1000x = 76.076.

Step 3: Subtract x from both sides of the equation to eliminate the decimal portion:
1000x - x = 76.076 - 0.076,
999x = 76.

Step 4: Divide both sides of the equation by 999 to solve for x:
x = 76/999.

Therefore, the decimal 0.076 repeated indefinitely can be expressed as the fraction 76/999.