Decimal Numbers !

A Decimal Number is a number that contains a Decimal Point
decimals2.gif


Ordering Decimals

Ordering decimals can be tricky. Because often we look at 0.42 and 0.402 and say that 0.402 must be bigger because there are more digits. But no!
If you follow the following method you will see which decimals are bigger.
  • Set up a table with the decimal point in the same place for each number.
  • Put in each number.
  • Fill in the empty squares with zeros.
  • Compare using the first column on the left, and pick out the highest in order.
  • If the digits are equal move to the next column to the right until one number wins.

Now,go practise with this special ordering decimals game


Adding Decimals

Adding decimals is easy if you keep your work neat
To add decimals, follow these steps:
  • Write down the numbers, one under the other, with the decimal points lined up
  • Put in zeros so the numbers have the same length
  • Then add normally, remembering to put the decimal point in the answer
Example:Add 1.452 + 1.3
Line the decimals up:


1.452


+
1.3




"Pad" with zeros:


1.452


+
1.300




Add:


1.452


+
1.300







2.752

Subtracting Decimals

Subtracting decimals is easy if you keep your work neat
To subtract decimals, follow these steps:
  • Write down the two numbers, one under the other, with the decimal points lined up.
  • Add zeros so the numbers have the same length
  • Then subtract normally, remembering to put the decimal point in the answer
Example: Subtract 1.1 - 0.03
Line the decimals up:


1.1


-
0.03




"Pad" with zeros:


1.10


-
0.03




Subtract:


1.10


-
0.03







1.07

Multiplying Decimals

Multiply without the decimal point, then re-insert it in the correct spot!

How to Multiply Decimals

Just follow these steps:
  • Multiply normally, ignoring the decimal points.
  • Then put the decimal point in the answer - it will have as many decimal places as the two original numbers combined.
In other words, just count up how many numbers are after the decimal point in both numbers you are multiplying, then the answer should have that many numbers after its decimal point.
Example: Multipy 0.03x1.1
start with:

0.03 × 1.1
multiply without decimal points:

3 × 11 = 33
0.03 has 2 decimal places,
and 1.1 has 1 decimal place,
so the answer has 3 decimal places:

0.033

Just remember: the answer should have the same number of decimal places as are in both the numbers you are multiplying.

Dividing Decimals

Quick method: use Long Division without the decimal point,

then re-insert the decimal point in the answer.


Dividing a Decimal Number by a Whole Number

To divide a decimal number by a whole number:
  • Use Long Division (ignoring the decimal point)
  • Then put the decimal point in the same spot as the dividend (the number being divided)


Dividing by a Decimal NumberBut what if you want to divide by a Decimal Number?
The trick is to convert the number you are dividing by to a whole number first, by shifting the decimal point of both numbers to the right:
move decimals
move decimals
Now you are dividing by a whole number, and can continue as normal.
It is safe to do this if you remember to shift the decimal point of both numbers the same number of places.