select the correct answer.\nwhat is the fractional form of $0.\\overline{02}$?\na. $\\frac{2}{99}$\nb…

select the correct answer.\nwhat is the fractional form of $0.\\overline{02}$?\na. $\\frac{2}{99}$\nb. $\\frac{1}{11}$\nc. $\\frac{2}{100}$\nd. $\\frac{1}{12}$

select the correct answer.\nwhat is the fractional form of $0.\\overline{02}$?\na. $\\frac{2}{99}$\nb. $\\frac{1}{11}$\nc. $\\frac{2}{100}$\nd. $\\frac{1}{12}$

Answer

Explanation:

Step1: Assign variable to decimal

Let $x = 0.\overline{02}$, which means $x = 0.020202...$

Step2: Eliminate repeating decimals

Multiply $x$ by 100 (since 2 digits repeat): $100x = 2.020202...$

Step3: Subtract to solve for x

Subtract original $x$ from $100x$: $100x - x = 2.020202... - 0.020202...$ $99x = 2$ $x = \frac{2}{99}$

Answer:

A. $\frac{2}{99}$