how do you convert repeating decimals into a fraction?

first you let the given number equal xeg x = 0.8989898989. equation 1then look at the decimal and figure out which number is repeating. here it is 89 a two digit numberso we multiply x and the decimal by 100. if the repeating number had 3 digits we would multiply by 1000, if 4 then by 10,000. the idea is to get it so that one repeat of the numbers is on the left of the decimal.so we have100 x = 89.89 equation 2if we take equation 1 from equation 2 we get 99 x = 89. finally if we divide by 99 we getx = 89/99 and as we said before x equals are decimal so the decimal in fraction form is 89/99.