First, we let x be the number. Since x is a repeated decimal, we need to get rid of the repeated 6. So we times 1000 to x:
1000x = 416.6666...
Then we multiply 100 to x:
100x = 41.66666...
Now, we can subtract them:
1000x - 100x = 900x
416.6666... - 41.66666... = 375
900x = 375
Divide both sides by 900:
x = 375/900
It just needs to be simplified:
375/900 = 75/180 = 15/36 = 5/12
So,
0.41666666666 = 5/12
