A survey reported that 63.63% of moviegoers prefer action films. This percent represents a repeating decimal. write is as a fraction?

Let x = 63.63 ... (by repeating i assume you mean the 63 is repeated as 63.636363 ...)

therefore 100x = 6363.63 ...

100x-x = 6300 (the recurring bit has been cancelled out which is what you should always aim to do)

99x=6300

x = 6300/99

cancel down

x = 700/11