0.1717 Repeating as a Fraction
What is 0.1717 Repeating?
0.1717 repeating is a decimal number that has a repeating pattern of digits. The "repeating" part means that the sequence of digits "17" keeps repeating indefinitely. This type of number is also known as a repetitive decimal or a non-terminating decimal.
Converting 0.1717 Repeating to a Fraction
To convert 0.1717 repeating to a fraction, we can use the following steps:
Step 1: Let x = 0.1717...
Let x = 0.1717...
Step 2: Multiply by 100
Multiply both sides of the equation by 100 to get rid of the decimal point:
100x = 17.1717...
Step 3: Subtract the Original Equation
Subtract the original equation from the new equation:
100x - x = 17.1717... - 0.1717...
This simplifies to:
99x = 17
Step 4: Divide by 99
Divide both sides of the equation by 99:
x = 17/99
The Final Answer
Therefore, 0.1717 repeating as a fraction is:
17/99
This fraction is a simplified form of the original decimal number. It's a useful way to express the repeating decimal as a ratio of two integers.
