This will explain how to convert:
Decimals to Fractions
Fractions back to Decimals
Step 1: The conversion
see the chart below
To make it easier think of it this way:
the ones place is x/1, place just to the right of the decimal is x/10, the next place to the right is x/100, etc...
For each place the you move to the right of the decimal add another zero (0) to the denominator.
so 0.5 = 5/10, 0.006 = 6/1000, 0.0004 = 4/10000
Step 2: What about a decimal with more than one numeral???
For example: If the decimal is 0.0023 you would go to the largest place (the 4th place in this case) and use that as your denominator (4th place= x/10000). The numerator is the numerals in the decimal(23 in this case). So for the decimal 0.0023, the fraction would be 23/10000.
Step 3: Simplifying a Fraction
if you need help with the GCF see step 1 and 2 of this instructable by Phoenixsong.
Ex: The GCD of 60/140 is 20. 60/2=3 and 140/20=7. The new simplified fraction is 3/7.
Step 4: Fraction back to a decimal
So to find the equation for converting two-thirds (2/3) into a decimal. You would take a(2) and divide it by b(3).
(If you don't know how to divide look at this instructable by TechnoGeek95.)
Step 5: Types of Decimals
This is called a repeating decimal it goes on forever repeating the same digits over and over.
ex: 0.66666...., 0.123123123..., 0.104710471047...
to simplify this number you have two options.
1)put a line over the repeating digits
2)round the decimal off
Another type of decimal is a terminating decimal.
A terminating decimal is a decimal that stops.
ex: 1/8 = 0.125, 1/50 =0.02, 1/32 = 0.03125
The third type of decimal is a irrational decimal.
An irrational decimal is one that does not terminate or repeat.
ex: pi, the square root of 2, any other non-perfect square roots
To simplify this number you can:
1) Round it off to whatever place you choose.