Division with Decimals

To master division with decimals, you have to become very familiar with exponents and place values. The equation of a decimal being divided is the decimal being divided by the power of ten. Depending on the exponent is how many times you move the decimal place to the left to get your answer.
Example: 5.06 divided by 10 ^ 4 = .000506
No matter if the exponent is negative of positive the decimal still moves to the left.

9's TRICK:
If any number is over 9, 99, 999, 9999, etc. that number will be repeated in the decimal form. It just depends on the place value of the 9.
1/9 = 0.11111111....
8/9 = 0.8888888...
* The pattern changes when the place value of 9 changes:
7/99 = 0.0707070707...
        - the 0 represents the missing tens place value in the number 7
37/99 = 0.3737373737.....
        - Notice how the 0 was replaced but a 3, because 37 has a number in the tens place.
* The pattern changes once again when the place value of 9 gets larger:
49/999 = 0.049049049049...
       -Once again the 0 is representing how the number 49 does not have a number in the hundreds place
749/999 = 0.749749749749...
       - The 0 was replaced with 7 because that us the number in the hundreds place.

***The reason why this numbers constantly repeat is because the number .999999 is actually equal to 1.

Converting Decimals to Fractions:
Method #1:
0.27777....
= 0.2 + 0.7777...              ( separate the lonely number from the repeating number)
= 2/10 + 0.777...   
= 2/10 + 0.777... / 10
= 2/10 + 7/9 * 1/10         (just found out any repeating number is over a 9 number)
= 2/10 + 7/90
= 18/90 + 7/90                (common denominator multiply 2/10 by 9)
= 25/90

Method #2:
0.4191919...
10n = 4.191919...
100n = 41.91919...
1000n = 419.191919...
* you want to get two answers that have the same repeating decimal. (in this case 10n and 1000n do)
1000      =     419.191919...
- 100      =         4.191919...
   990             415
The answer then comes to 415/990