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*Contributor: Briana Pincherri. Lesson ID: 11353*

Uh oh! You have to multiply decimal numbers, but the decimal points don't line up! Don't panic. It's easy! Learn how to place decimals in your product!

categories

subject

Math

learning style

Visual

personality style

Lion, Otter

Grade Level

Intermediate (3-5)

Lesson Type

Quick Query

- What do the following items have in common?

Each of these was used to solve arithmetic problems before calculators were invented!

- How would you set up and solve the problem 1.23 x 45.6 without a calculator?

Drop that abacus and learn how to do it yourself with pen and paper!

When you multiply decimals, you may assume that you would line up the decimal points and bring them right down in the same location in your answer.

However, if you did this, you would be INCORRECT!

That logic works perfectly for adding and subtracting decimals, but it isn't needed when multiplying them.

- So, what do you do?

Well, take a look!

When you are multiplying decimals, follow these steps.

- Rewrite the problem vertically and multiply like normal. Ignore the decimal points.

- Count how many numbers were behind each decimal in the problem to start.

- Make sure the product has the same amount of numbers behind the decimal as the
*sum*of numbers behind decimals in the problem.

NOTE: When you rewrite the problem vertically (on top of each other), you should put the number with the most digits on top. Remember, the decimals DO NOT have to line up!

Example

2.2 x 1.12

1 | . | 1 | 2 | ← Number with more digits goes on top. | |||

x | 2 | . | 2 | ||||

2 | 2 | 4 | |||||

+ | 2 | 2 | 4 | 0 | |||

2 | 4 | 6 | 4 | ||||

2 | . | 4 | 6 | 4 | Count how many numbers are behind the decimal in the problem. There are 3, so move the decimal over 3 places in the answer. |

As you can see in the above example when you rewrite the problem to multiply, you put the number with more digits (the longer number) on top. Then, you can ignore the decimal(s) and multiply like you know how.

Once you get to your answer, you must decide where the decimal should go.

To figure it out, count how many digits were behind the decimal in the original problem. You will move your decimal place over that many spots in your answer.

DONE!

Continue to the *Got It?* section to take a further look and complete some practice problems!