Final answer:
The rational number equivalent to 0.17 repeating is 17/99.
Step-by-step explanation:
The number 0.17 repeating can be represented as a rational number. In order to express it as a rational number, we need to convert the repeating decimal into a fraction. Let's call the number x:
x = 0.17171717...
Multiply both sides of the equation by 100 to move the decimal point two places to the right:
100x = 17.17171717...
Subtract the original equation from the new equation to eliminate the repeating part:
100x - x = 17.17171717... - 0.17171717...
Simplify the equation:
99x = 17
Divide both sides of the equation by 99:
x = 17/99
So, the rational number that is equivalent to 0.17 repeating is 17/99.