Why do you move the decimal point the same number of places in the dividend and the divisor?

That is because if you do the same thing to the divisor as the dividend then nothing changes. Say you have 2 divided by 4; if you multiply both by 10 you have 20/40 which is the same thing. So if you have 2.36 divided by 4.19 that is the same as 236/419 since you multiplied both by 100.