Division and converting decimals to fractions

Division powers of ten

Example: 4.07 / 10^2 = 0.0407
               Check by doing this: 4.07 x 10^-2 [4(1) + 0(10^1) + 7(10^-2)] (10^-2)
Example: 78.392 / 10^7 = 0.0000078392
               A positive exponent moves the decimal to the left that many places, and moves the decimal to the right if the exponent is negative.

Converting Decimals to Fractions

Helpful Hints
-  0.11111... = 1/9
-  0.01010... = 1/99
-  0.001001... = 1/999

A number over the fraction of 9 is repeating.
Examples:
2/9 = 0.2222...
3/9 = 1/3 = 0.3333...
4/9 = 0.4444...
5/9 = 0.5555...
6/9 = 2/3 = 0.6666...
7/9 = 0.7777...
8/9 0.8888...
25/99 = 0.25252525

To write a repeating decimal into a fraction, there are two ways.

One way is:

Another way is:

More ways of converting decimal examples are:
0.47 = 47/100
0.028 = 28/1000
0.777... = 7/9
0.2121... = 21/99