When $0.\overline{47}$ is converted into a fraction, the result is

Concept & Formula To convert a pure recurring decimal to a fraction, write the repeated sequence as the numerator and place as many $9$s in the denominator as there are digits in the repeating sequence. $$ 0.\overline{pq} = \frac{pq}{99} $$ Step-by-Step Solution Given the decimal: $0.\overline{47}$ Here, the repeating sequence is $47$, which consists of exactly two digits. Therefore, we place the number $47$ in the numerator and two $9$s in the denominator. $$ 0.\overline{47} = \frac{47}{99} $$ Exam Strategy & Shortcut For pure recurring decimals (where the bar starts immediately after the decimal point), simply count the digits under the bar. The number of digits equals the number of $9$s in the denominator. This can be answered visually in 2 seconds without writing anything down. Common Pitfall A common error is confusing pure recurring decimals with terminating decimals or mixed recurring decimals, leading students to choose a denominator of $90$ or $100$ (like option a or c). Always verify where the recurring bar begins and ends. Final Answer Therefore, the correct answer is $\frac{47}{99}$.