But not every number is a whole number. What if you had less than 1 of something: less than 1 dollar, less than one whole football game; less than 1 one apple? How would you talk about that part?

The decimal system lets us write numbers of all types and sizes. How? We use that little dot, called the decimal point!

50 = half

25 = one fourth

Every number to the right of the decimal point is less than one.

Every number to the left of the decimal point is a whole number. 

You can understand the concept easily with money.

$5.65 = 5 whole dollars with 65 cents (parts of a dollar) left over.

In the decimal number system, the value of a digit of the number depends on its place, or position, in the number. The digit to the left of the decimal point has the value of ones, or 0-9. The values move by multiples or ten.

To the left, you multiply by 10.

As you move to the right of the decimal point, the value of each place (place value) is divided by 10. We use the "th" ending for those numbers to show they are parts.

To add or subtract with decimals, just keep the decimal points aligned (below or above each other). Then place the decimal point directly under in the total. NOTE: the decimal point is immediately after a whole number.

Multiplying with decimals

1. Multiply the numbers just as if they were whole numbers.

• Line up the numbers on the right - do not align the decimal points under each other!
• Starting on the right, multiply each digit in the top number by each digit in the bottom number, just as with whole numbers.
• Add the products, just like you would with whole numbers.

2. Count the number of decimals to the right of the decimal point of both the numbers being multiplied.
3. Place the decimal point in the answer. Start on the right and count the total number of decimals you added.
4. Multiply the numbers just as if they were whole numbers.

• Line up the numbers on the right - do not align the decimal points.
• Starting on the right, multiply each digit in the top number by each digit in the bottom number, just as with whole numbers.
• Add the products.

2. Place the decimal point in the answer by starting at the right and moving a number of places equal to the sum of the decimal places in both numbers multiplied.

To divide decimal numbers:

1. If the divisor (number on the left) is not a whole number, move decimal point to right to make it a whole number. Then move decimal point in dividend (number on the right) the same number of places.
   
    
2. Divide as usual. Keep dividing until the answer finishes or repeats.
   
    
3. Put the decimal point directly above decimal point in the dividend.
   
    
4. Check your answer. Multiply quotient by divisor. Does it equal the dividend?

Now you try it!

1.  146 - 98.3 = 47.7

2.  398.43 ÷ 398.43 = 15.56

3.  487.41 + 54.67 =   542.08

4.  42.9 X 2.5 = 107.25

ANSWERS 1: 47.6; 2. 15.56; 3. 542.08; 4. 107.25