We are asked to convert the repeating decimal to fraction
[tex]\text{Take d = 4.}\bar{\text{72}}\text{ = 4.72727272}\ldots[/tex][tex]\text{ d = 4.72727272}\ldots\text{ (first equation)}[/tex]
Step 1: Multiply both sides by 100 because there are two repeating digits
[tex]\text{ 100d = 472.727272}\ldots(\text{second equation)}[/tex]
Step 2: Subtract the first equation from the second one
[tex]\begin{gathered} \text{ 100d -d = 472.727272 - 4,72727272} \\ \text{ 99d = 467. 99999}\ldots\text{ }\approx\text{ 4}68 \\ \text{ 99d = 4}68 \\ \text{ d =}\frac{468}{99}=\frac{52}{11} \end{gathered}[/tex]
Therefore, the fractional form of the repeating decimal 4.7277272... is 52/11
