Write each repeating decimal as a quotient of integers.

Question

.217 repeating

Answer 1

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.