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What is 0.17 repeating as a rational number, simplified?

1 Answer

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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.

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