# Addition, Subtraction, Multiplication, and Division with Decimal Notation

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: Adding and Subtracting Decimals: Examples & Word Problems

### You're on a roll. Keep up the good work!

Replay
Your next lesson will play in 10 seconds
• 0:07 Decimal Notation
• 2:06 Multiplication with…
• 3:07 Division with Decimal Notation
• 4:15 Lesson Summary

Want to watch this again later?

Timeline
Autoplay
Autoplay

#### Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Jennifer Beddoe
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.

To unlock this lesson you must be a Study.com Member.

### Register for a free trial

Are you a student or a teacher?

#### See for yourself why 30 million people use Study.com

##### Become a Study.com member and start learning now.
Back
What teachers are saying about Study.com

### Earning College Credit

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.