2. The repeating decimal \( 0.141414 \ldots \) can be expressed as a fraction this question for review

To convert the repeating decimal \( 0.141414 \ldots \) into a fraction, let's assign it a variable: let \( x = 0.141414 \ldots \). Then, multiplying both sides by 100 (since the repeat is two digits long), we get \( 100x = 14.141414 \ldots \). Now, subtract the first equation from the second: \( 100x - x = 14.141414 \ldots - 0.141414 \ldots \). This simplifies to \( 99x = 14 \), leading us to \( x = \frac{14}{99} \). Voilà, the repeating decimal becomes the fraction \( \frac{14}{99} \)! If you want to explore more about periodic decimals, remember there are whole series of decimals to tackle! This process of converting other recurring decimals works similarly: identify the repeating section, set up the equation, and voila! You’ll be impressively converting them all into fractions in no time, just like a math magician!