Question

The rational form of the number \( 1.41 \overline{41} \) is

• A. \( \frac{154}{99} \)
• B. \( \frac{55}{99} \)
• C. \( \frac{140}{99} \)
• D. \( \frac{41}{99} \)

Hint:

For repeating decimals, let the repeating part be \( y \), express it as a fraction, and add it to the non-repeating part to get the rational form.

Answer 1

The Correct Option is C

Step 1: Express the given decimal as a rational number.
The given number is \( 1.41 \overline{41} \), which can be written as: \[ x = 1.414141\ldots \] Let \( y = 0.\overline{41} \), so \( y = \frac{41}{99} \). Therefore, the rational form of the given number is: \[ 1 + \frac{41}{99} = \frac{140}{99}. \]
Step 2: Conclusion.
Thus, the rational form is \( \frac{140}{99} \), corresponding to option (C).