Question

1. which number is equivalent to 2.\overline{42}?

a. \frac{1}{21}
b. 2\frac{21}{50}
c. 2\frac{19}{45}
d. 2\frac{14}{33}

Explanation:

Step1: Let \(x = 2.4242\cdots\)

Let \(x=2.4242\cdots\). Then \(100x = 242.4242\cdots\) since moving the decimal point two places to the right for a repeating - decimal with a two - digit repeating part.

Step2: Subtract \(x\) from \(100x\)

\(100x−x=(242.4242\cdots)-(2.4242\cdots)\). This simplifies to \(99x = 240\) because the repeating parts cancel out.

Step3: Solve for \(x\)

\(x=\frac{240}{99}=\frac{80}{33}=2\frac{14}{33}\)

Answer:

D. \(2\frac{14}{33}\)