The word decimal comes from the Latin decem, meaning "ten". Consider the number 123.864. The digits in this number correspond to place values: Notice the powers of 10: The place values are named for the powers of 10. As you move to the left in the chart above, each position is ten times larger. As you move to the right, each position is ten times smaller.

Working with Decimals:

When adding decimal numbers, line up the decimal points. If no decimal point is visible, the decimal is behind (to the right of) the number.

Add: 34.5 + 5.87 + 30

 Notice the location of the decimal in the number 30. Notice the use of place holding zeros to help keep the alignment straight.
SUBTRACT
When subtracting decimals, line up the decimal points. Using place holding zeros will be important as a visual reminder to subtract all positions.

Subtract: 35 - 4.62

 Notice the location of the decimal in the number 35. Notice the use of place holding zeroed as a reminder to subtract. You cannot just drop down the .62 into your answer.

MULTIPLY
Multiply as if the decimal points were not present.
When finished,
count up how many numbers are after the decimal points in BOTH numbers. This count is how many numbers are needed after the decimal point in your answer.

Multiply: 3.45 x 2.136

 There are 2 number after the decimal point in 3.45. There are 3 numbers after the decimal point in 2.136. Since 2 + 3 = 5, the decimal point will be placed such that 5 numbers appear after decimal point. Yes, the answer can be written as 7.3692.
DIVIDE
When dividing decimal numbers, move the decimal point in the number you are dividing by to create a whole number. Now, move the decimal point in the number being divided by this same number of places.

Divide: 34.5 รท 1.25

 Notice that the decimal point under the division sign is located in its new position. If necessary, additional zeros can be placed to the right of the decimal point to continue the division. The decimal point is placed above its new location in the answer.