



 
Savanna, I am going to convert 0.13777... into a fraction and you can use the same technique for your problem. Let d = 0.13777... and then perform the subtraction
Multiply both sides by 100 to eliminate the decimal point
and hence
You can check this by having your calculator find 31/225. I multiplied both sides of d = 0.13777. by 10^{1} = 10 because the repeat is 1 digit long. If the repeating fraction were 0.13757575... so that the repeat (75) is two digits long I would let d = 0.13757575... and multiply both sides by 10^{2} = 100 before subtracting. Try it and use your calculator to check your answer. If the repeat were 3 digits long I would multiply by 10^{3} = 1000 and so on. I hope this helps,  


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