Whew, that's a lot of subject matter to cover in an Answers forum; but here are the conversion operations in a nutshell.

To change a fraction into a decimal, divide the numerator (top) of the fraction by the denominator (bottom) of the fraction. For example, to change 3/8 to a decimal, divide 3 by 8:

__.375_

8 )3.000

-2 4

----

60

-56

---

40

-40

----

0

Therefore, 3/8 = 0.375

For a mixed number like 2 3/8, it's easiest to convert it to an improper fraction, 2 3/8 = 19/8, then do the division.

To change a decimal into a fraction, you have to know the place-values of each decimal position. The first place after the decimal is tenths (1/10), the second place is hundredths (1/100), the third place is thousandths (1/1000), and so on.

A decimal such as .375 then is 3/10 + 7/100 + 5/1000 = 300/1000 + 70/1000 + 5/1000 = 375/1000. Note that this is just the three numbers, 375, divided by the lowest decimal place value, 1/1000.

You can reduce the fraction as follows: 375/1000 = 3*125/8*125 = 3/8

Hope that helps some.