Question

Find the rational number whose decimal expansion is 0.3344444

Answer 1

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