write the following infinite decimal expansion as a fraction 0.366
To write the infinite decimal expansion 0.366 as a fraction, we can use the following steps:
Step 1: Let x = 0.366.
Step 2: Multiply both sides of the equation by 1000 (to move the decimal point three places to the right since there are three digits after the decimal point).
We get 1000x = 366.
Step 3: Subtract x from both sides of the equation.
We get 999x = 366.
Step 4: Divide both sides of the equation by 999 to solve for x.
x = 366/999.
Therefore, the fraction equivalent of the infinite decimal expansion 0.366 is 366/999.