Answer:Therefore, x = [tex]\frac{2291}{990}[/tex].Step-by-step explanation:Given : 2.314 (14 repeating) .To find : Express as a fraction .Solution : We have given 2.314 (14 repeating) .Let x = 2.31414141.......On multiplying both sides by 100100x = 100 * 2.31414141....100x = 231.414141......We can express 231.414141...... in term of x .100x = 229 .1 + 2.31414141.......100x = 229.1 +x On subtracting both sides by x .100 x -x = 229 .199x = 229.1On dividing both sides by 99x= [tex]\frac{229.1}{99}[/tex].x = [tex]\frac{2291}{990}[/tex].Therefore, x = [tex]\frac{2291}{990}[/tex].