0.41666666666 as a fraction

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