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DECIMALS

MEANING OF DECIMALS

Example: the numbers we use in everyday life are decimal numbers, because there are 10 of them (0,1,2,3,4,5,6,7,8 and 9).

Often "decimal number" is also used to mean a number that uses a decimal point followed by digits that show a value smaller than one.

Example: 45.6 (forty-five point six) is a decimal number.

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STEPS IN ADDING AND SUBTRACTING DECIMALS

Adding:

Ex.1) 13.6 + 17.8

Step 1: Line up the decimal points so that similar place values are lined up. In other words, the tens place in both numbers should be lined up, the ones place in both numbers should be lined up, etc.

Step 2: Add the digits together that are lined up.

Ex. 2) 14.86 + 22.9

If the numbers do not have the same number of digits after the decimal point, you can use "filler zeros" to help you line up the numbers.

Ex 3.) 45 + 6.98

A common mistake that is often made is that the 45 is added to the 98. However, here the 45 represents a whole number. It is 4 tens and 5 ones. The 98 represents 9 tenths and 8 hundredths. These numbers do not hold the same place values.

So instead, we can add a decimal point at the end of the 45 and then add two filler zeros so that the numbers can be lined up.

45.00 + 6.98

Now we are ready to solve:

Subtracting:

The steps for subtracting numbers with decimals are exactly the same as adding decimals. Let's take a look at a couple of examples.

Ex. 4) 239.83 - 125.51

First we will line up the numbers by making sure the decimals are lined up. Then we just subtract the numbers that are in common place value positions.

Ex. 5) 98.3 - 45.67

We will start by lining them up.

In the subtraction examples, the filler zeros are even more helpful. Some make the mistake of placing a 7 in the hundredths place of the answer. However, take a look at what happens with the filler zero....