Decimals
The Decimal System
1000 thousands 
100 hundreds 
10 tens 
1 ones 
\(\frac{1}{10}\) tenths 
\(\frac{1}{100}\)
hundredths 
\(\frac{1}{1000}\)
thousandths 
Decimal notation can be used to give an 'alternative' way of expressing a fraction
Example :
'two  tenths' = \(\frac{2}{10}\) = 0.2 'two  hundredths' = \(\frac{2}{100}\) = 0.02 'twothousandths' = \(\frac{2}{1000}\) = 0.002 
Staring off with something you know already, like decimal currency, would be a good starter.
You are probably aware, at least subconciously, that 25 pence (i.e. 0.25 pounds) is equal to a quarter of a pound  so you can already convert between some decimals and fractions.
The BBC have an introductory site  click here
Transforming Decimals into Fractions
Method

Examples

0.054 = \(\frac{54}{1000}\) = \(\frac{27}{500}\) 
2.75 = \(2 \ \frac{75}{100}\) = \(2\ \frac{3}{4}\) 
5.8 = \(5\ \frac{8}{10}\) = \(5\ \frac{4}{5}\) 
You can see the logic 
 if you have one decimal place, you put the 'decimal part' over 10
 if you have two decimal places you put the 'decimal part' over 100
 if you have three decimal places, you put the 'decimal part' over 1000
and so on.
And then reduce to lowest terms, where appropriate.

Transforming Fractions into Decimals
Method
A fraction can also be considered as a division
For example :
can be considered as either
This division will produce the required decimal form of the fraction.
The process of transforming fractions into decimals is quite straightforward. The line separating the numerator from the denominator can also be considered as denoting division  so divide the numerator by the denominator (that's all there is to it, although, in general, you are going to get a large number of decimal places  so you will have to decide how many decimal places you want in the answer) 
Examples
3/4 = 3÷ 4 = 0.75 41/8 = 41÷ 8 = 5.125 2/3 = 2 ÷ 3 = 0.666......... (recurring) 1/7 = 1 ÷ 7 = 0.142857142857.. (could say 0.143 to 3 dec. places, for example) 
It is a mathematical fact that this division will always produce a
recurring decimal.
Sometimes, this recurring decimal will just be of the form
0.250000000......
where the 'zeros' recur, which will conventionally just be written as
Sometimes, a nonzero number recurs
And sometimes a group of numbers recur
This shows why a number like p cannot be represented as a fraction  because when represented as a fraction it does not recur.
Common conversions worth memorizing
\[\frac{1}{2} =0.5 \] 
\[\frac{1}{4} =0.25 \] 
\[ \frac{1}{8}= 0.125 \] 
and multiples of these, e.g : \(\frac{3}{8} = 0.375\)

Multiplying and Dividing Decimals by Powers of 10
 Multiplying a decimal by a multiple of 10 shifts the
decimal point a number of places to the right .
 The number of places is equal to the index of 10
 or alternatively (if you are not knowledgeable about indices), the number of places
is equal to the number of zeroes in the multiplier
 a multiplier of 10 > 1 place
 a multiplier of 100 > 2 places
 a multiplier of 1000 > 3 places
 etc. etc.
Example
\[ 1.275 \times 10 =12.75\] \[1.275 \times 100=127.5\] \[1.275 \times 1000=1275\]  Dividing a decimal by a multiple of 10 shifts the
decimal point a number of places to the
left.
The logic is directly analogous to that for multiplication by 10
 The number of places is equal to the index of 10, although ignoring the minus sign.
 or alternatively (if you are not knowledgeable about indices), the number of places
is equal to the number of zeroes in the divisor
 a divisor of 10 > 1 place
 a divisor of 100 > 2 places
 a divisor of 1000 > 3 places
 etc. etc.
Example
1.275 ÷ 10 = 0.1275 1.275 ÷ 100 = 0.01275 1.275 ÷ 1000 = 0.001275

Multiplying Decimals
Prior knowledge required : Long multiplication (in Basic Arithmetic)
Method

Examples

With respect to the last example in the second column, there are a total of four decimal places originally : (three in 0.006, and one in 0.2), so
 Step 1 : Multiply 6 × 2 = 12
 Step 2 : Adjust this 12, by shifting the decimal point by four places to the left \(\rightarrow$ 0.0012

Dividing Decimals
Prior knowledge required : Long Division (in Basic Arithmetic)
 To
divide a decimal by an
integer
This is very similar to division of an integer by an integer. Use the same method, but in this case, ensure that the position of the decimal point is retained Example
63.2

12 ) 758.4The decimal point in the answer is placed above the decimal point in the dividend.  To
divide a decimal by a
decimal
 Multiply both decimals by the smallest power of 10 which will make the divisor (second decimal ) into an integer.
 Perform the division as in the the previous example )
Examples
6 ÷ 0.2 = 60 ÷ 2 = 30 6 ÷ 0.02 = 600 ÷ 2 = 300 6 ÷ 0.002 = 6000 ÷ 2 = 3000 60 ÷ 0.02 = 6000 ÷ 2 = 3000 0.006 ÷ 0.02 = 0.6 ÷ 2 = 0.3 Another Example
5.642 ÷ 0.13 = 564.2 ÷ 13 and then solve as already described
Note particularly that it is only necessary to make the divisor into an integer. It
is not necessary that both numbers should be integers.

Addition and Subtraction of Decimals
Method

Examples


Rounding to n Decimal Places
Method

Examples


Rounding to 'n' Significant Figures
The first significant
figure is the first nonzero
digit
Method

Example


Links to Other Sites
 All About Decimals : links to about two dozen seperate areas.