Given that 7/9 = 0.77777777 (recurring) convert 0.27777777(recurring) into a fraction. Give your answer in the simplest form.

if 7/9 = 0.777777 then 0.0777777 must be equal to 7/90 as it is a tenth of the original number. 0.2= (2/10)(7/90) + (2/10) = 0.27777777 find the lowest common multiple: 90, then make the denominators of each fraction this value via multiplication, multiplying the numerators by the same amount. This results in....(7/90)*1=(7/90) and (2/10)*9=(18/90). Now that the denominators are the same you can find the sum of the fractions by adding the numerators... 7+9=16 thus (7/90) + (2/10) = (25/90). Now to get the fraction in its simplest form you must find the highest common factor between the new numerator and denominator. In this case it is 5 (can be found by looking at all of 25's factor pairs and determining whether 90 is divisible by the amount). Therefore 0.27777777 in its simplest form is...(25/90)/2=(5/18)