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Jennifer has an MS in Chemistry and a BS in Biological Sciences.

Performing operations such as addition, subtraction, multiplication and division has some differences when there are decimals involved. This lesson will explain how to perform these operations all while keeping the decimals straight.

Decimal Notation

The decimal number system is the most common system of counting in the world. It is a base 10 system, which means that it is based on a 10 number cycle, the numbers 0 - 9. Each number is also divided into 10 sections and so on and so on. These sections are notated by a decimal point, which is a dot placed after the number in the one's place and before the number representing the number of sections of the next number. The number after the decimal point represents a fraction of a number with the base of 10.

For example, 2.2 is a number written in decimal notation depicting 2 whole numbers and 2/10's of another whole number. And 37.55 is 37 whole numbers and 55/100's of another whole number.

Addition and Subtraction with Decimal Notation

When adding or subtracting whole numbers, you just line them up on the right and add (or subtract).

For example:

25 + 13 = 38

or

59 - 22 = 37.

Numbers that include decimals are different. You can't just line them up and add. If you do that, you end up with the following:

41.78 + 13.2 is equal to 43

It's easy to see how this is not right. When adding or subtracting with decimals, the numbers need to line up along the decimals. It doesn't matter how many numbers are on either side of the decimal. That is where they need to line up to get the correct answer. Let's do the problem from above correctly. If you need to, you can add zeros at the end of a number to make sure there are two numbers in each column.

41.78 + 13.20 is equal to 54.98.

This way, you will get the right answer every time without trouble.

Multiplication with Decimal Notation

Multiplying numbers that include decimal notation is different as well. Setting up the multiplication problem is the same, but then the decimal has to be figured into the answer.

Let's try an example:

13.9 * 7.12

The first step is to perform the multiplication as you would with any multiplication problem.

Next, you count the number of decimal places in the two numbers being multiplied together. 13.9 has one decimal place and 7.12 has 2, for a total of three decimal places. This is how many decimal places will be needed in the answer.

The last step is to place the decimal in the correct place. For this problem, it must be placed 3 spaces from the right, because that is the total number of spaces to the right of the decimal in the two numbers being multiplied together.

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So, the answer to this multiplication problem is 98.968.

Division with Decimal Notation

Before we talk about how to divide with decimals, it will be helpful to review the division terms.

In a division problem, the divisor is the number you divide by. The dividend is the number you divide into, and the quotient is the answer to the division problem.

When performing division problems when the divisor is a decimal, there are certain steps that need to be followed.

Let's look at this example:

24.6 divided by 1.2

The first step to performing this division problem is to move the decimal place all the way to the right on the divisor. There cannot be a decimal in the divisor to work a division problem.

Because you have moved the decimal point in the divisor, in order to keep the equation equal, you must also move the decimal point the same number of places in the dividend.

This changes the division problem to this:

246 divided by 12, which can be easily solved. The answer to this division problem is 20.5

Lesson Summary

Performing simple operations such as addition, subtraction, multiplication or division is made a bit more complex when decimals are involved. By remembering the simple rules, working with decimals should be an easy proposition. These rules include: lining up the decimals in addition and subtraction, moving the decimal in the divisor in division, and proper decimal placement in the answer to a multiplication problem.

Learning Outcome

After viewing this lesson, you could know how to perform addition, subtraction, multiplication, and division operations with decimals by lining them up correctly.

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