Firstly, we need to define what a recurring decimal and a fraction are. A fraction is an expression in which a number is being divided by another number. The number at the top is called the numerator and the one at the bottom is called the denominator, for example ⅔. A recurring decimal is a decimal representation of a number whose digits are repeating its values at regular intervals infinitely. For example: 0.444444 is a recurring decimal. Now there are also types of recurring decimal, thus making the conversion to fraction slightly different for each type. Type 1: 0.5555555…. Step 1: Let x = recurring decimal in expanded form. x = 0.5555555…. Step 2: Let the number of recurring digits = n. Number of recurring digits in our case equals 1. Step 3: Multiply recurring decimal by 10^n. 10^n = 10 in our case because n=1. Hence, 10x= 10 × 0.55555555… = 5.55555…. Step 4: Subtract Step 1 from Step 3 to eliminate the recurring part and solve for x. 10x - x = 5.5555 - 0.5555 9x = 5 x = 5/9 Type 2: 0.1515151515…. Step 1: Let x = recurring decimal in expanded form. x = 0.15151515…. Step 2: Let the number of recurring digits = n. Number of recurring digits in our case equals 2. Step 3: Multiply recurring decimal by 10^n. 10^n = 100 in our case because n=2. Hence, 100x= 100 × 0.15151515… = 15.151515…. Step 4: Subtract Step 1 from Step 3 to eliminate the recurring part and solve for x. 100x - x = 15.151515 - 0.151515 98x = 15 x = 15/99 As the number of recurring numbers would increase the value of n would increase simultaneously.