Convert the following, repeating, decimal into a fraction in simplest form .17
To convert the repeating decimal 0.17 into a fraction, we follow these steps:
Step 1: Let x = 0.17.
Step 2: Multiply both sides of the equation by 100 to get rid of the decimal: 100x = 17.
Step 3: Subtract x from both sides: 100x - x = 17 - 0.17.
Simplifying, we have 99x = 16.83.
Step 4: Divide both sides by 99: (99x)/99 = 16.83/99.
This simplifies to x = 0.17 = 16.83/99.
Therefore, the fraction in simplest form is 16.83/99.