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Write the repeating decimal as a fraction.
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Q. Write the repeating decimal as a fraction.
- Define as decimal: Let be the repeating decimal We can write this as:
- Create equation with repeating part: To convert the repeating decimal to a fraction, we need to create an equation that isolates the repeating part. Since the digits repeat every three decimal places, we multiply by (which is ) to shift the decimal point three places to the right.So, we get:
- Subtract original x from x: Now we subtract the original x from the to get rid of the repeating decimals:This simplifies to:
- Divide by to find x: To find the value of x, we divide both sides of the equation by :
- Simplify fraction for : We can simplify the fraction by looking for the greatest common divisor (GCD) of and . The GCD of and is , so the fraction is already in its simplest form.
