Answer: The fraction 301/900 Note: I'm assuming the 4's continue on forever
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Work Shown:
I'm going to assume that the 4s go on forever. I'll represent this with three dots after the last 4 like so 0.334444...
Now let x = 0.334444...
Multiply both sides by 100 x = 0.334444... 100x = 100*(0.334444...) 100x = 33.444444...
And repeat with 1000 x = 0.334444... 1000x = 1000*(0.334444...) 1000x = 334.444444...
Then subtract and solve for x. Notice how the decimal parts line up and cancel 1000x-100x = (334.444444...) - (33.444444...) 1000x-100x = (334+0.444444...) - (33+0.444444...) 1000x-100x = 334+0.444444... - 33 - 0.444444... 1000x-100x = (334-33)+(0.444444... - 0.444444...) 900x = 334 - 33 900x = 301 x = 301/900
