How do you divide decimals by decimals?

Same way you divide whole numbers with whole numbers

1. Convert the divisor (number by which you are dividing) into a whole number by multiplying it by 10 enough times;
2. multiply the dividend (the number into which the divisor is being divided) by the same number of times of 10s;
3. the original division is the same as dividing the new dividend by the new whole number divisor.

eg divide 6.519 by 1.23

1. convert 1.23 to a whole number by multiplying twice by 10: 1.23 x 10 x 10 = 1.23 x 100 = 123
2. twice multiply 6.519 by 10 also: 6.519 x 10 x 10 = 6.519 x 100 = 615.9
3. 6.519 ÷ 1.23 = 516.9 ÷ 123 which can be calculated:

................ 5.3

........ ---------

123 | 651.9

........... 615

........... -----

.............. 36 9

.............. 36 9

.............. ------

..................... 0

Therefore 6.519 ÷ 1.23 = 5.3