Reference

Operations With Decimals

Method

Adding and Subtracting Decimals

The rules for adding and subtracting decimals are similar to the general rules for adding and subtracting integers. The most important point is to align the decimal points correctly. For example, consider adding the following decimal numbers.

3.4 + 12.802

There are three steps to finding this sum.

Line up the Decimal Points

The first step is to line up the decimal points. The sum is written so that the decimal points are on top of each other.

The numbers are now written vertically. A place value chart can also be used to align the decimal places.

Place Zeros at the End of a Decimal If Needed

The first number does not have the same number of decimal places as the second number. Place zeros so that the numbers have the same number of decimal places.

Inserting zeros after the decimal point for the number 3.4

Now that the decimal digits in each of the numbers are equal, it will be easier to add or subtract these numbers.

Add Digits with the Same Place Value

Temporarily ignore the decimal point and add the digits that have the same place value. This is the same as adding two integers. After that, bring down the decimal point.

The sum of the given numbers is

16.202 .

Note that the subtraction of decimals is done in the same way.

Method

Multiplying Decimals

Multiplying decimals has the same procedure as multiplying integers. The only difference is where the decimal point is placed in the product. The procedure will be demonstrated with an example.

1.69 \times 3.7

The following steps can be followed to multiply decimals.

Multiply Ignoring the Decimal Point

Ignore the decimal points for now and multiply the numbers as if multiplying integers.

Count the Number of Decimal Places in the Factors

After the numbers are multiplied, count the total number of decimal places in each factor.

The sum of the decimal places is

3 .

Locate the Decimal Point in the Product

The number of decimal places in the product is the sum of the decimal places in the factors. In the previous step, it was found that there were

3

decimal places in the example factors. This means that the product will have

3

decimal places as well.

The product of

1.69

and

3.7

6.253 .

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