Write each repeating decimal as a quotient of integers.
.217 repeating
To write .217 repeating as a quotient of integers, we can set up the following equation:
x = .217217217...
Next, multiply both sides of the equation by 1000 to get rid of the repeating decimal:
1000x = 217.217217217...
Now, subtract the equation x = .217217217... from 1000x = 217.217217217...:
999x = 217
Divide both sides by 999 to solve for x:
x = 217/999
Therefore, .217 repeating can be written as the quotient 217/999.