Multiplying Decimals: Rules, Steps and Examples

Multiplying Decimals: Rules, Steps & Examples

Do you know how to multiply numbers with more than one digit but when it's a decimal you forget what to do with the decimal point? This lesson teaches you the steps for multiplying decimals. Then see those steps in action through the use of examples.

Multiplying Decimals: Gas Prices

The Hernandez family is planning a road trip. Mr. Hernandez has figured that their car will use approximately 96 gallons of gas on the round trip. If gas is $3.45 per gallon, how much will the Hernandez family spend on gas? We know that gas costs $3.45 per gallon, and the Hernandezes will use 96 gallons. We'll need to multiply to find the total cost of the gas used. But, one of the numbers we'll multiply by has a decimal point in it. How will we do this?

First we should know that the decimal point is the symbol used to separate the whole number from the fractional part of a number, the tenths, hundredths, etc. In our equation $3.45 is the decimal. The decimal point separates the three whole dollars from the forty five cents.

Multiplying Decimals: Step By Step

Let's break this multiplication down into steps.

Step 1: Complete the multiplication as you normally would, as if the decimal was not there.

In this case, we're multiplying 96 by 3.45.

Start with the 6 in the ones place and multiply 6 by 345. Then, multiply the 9 in the tens place by 345, and add those products to get the final answer. Look back at the numbers we multiplied together.

Step 2: Determine the total number of digits after the decimal points in the numbers that you're multiplying together.

How many digits are to the right of the decimal point? In our problem 3.45 has two digits after the decimal point. 96 is a whole number and therefore, has

no decimal point in it. So, the numbers we're multiplying have a total of two digits after their decimal points.

Step 3: Place the same number of digits behind the decimal point in the product.

Since 3.45 and 96 have a total of two digits after their decimal points, we'll need two of the product's digits behind the decimal point. So instead of 33,120, the final product is actually 331.20. The Hernandez family will spend a total of $331.20 on gas during their road trip.

Multiplying Two Decimals

Let's go back to the Hernandez's road trip for another example. The Hernandezes actually used less gas than Mr. Hernandez had estimated. Their actual gas usage was 89.75 gallons. What was the actual cost of gas?

Let's follow our steps again:

Step 1: Complete the multiplication as you normally would, as if the decimals were not there.

In this case, we're multiplying 3.45 by 89.75.

Start with the 5 in the decimal 3.45 and multiply it by 89.75. Then continue on by multiplying the four and three as well. Keep your numbers lined up, and add to find the answer. Look back at the numbers you multiplied.

Step 2: Determine the total number of digits after the decimal points in the numbers you're multiplying together.

Ask yourself how many digits are to the right of the decimal point? 89.75 has two digits after the decimal point. 3.45 also has two digits after the decimal point. Our original numbers have a total of four digits after their decimal points.

Step 3: Place the same number of digits behind the decimal point in the product.

Since 89.75 and 3.45 have a total of four digits after their decimals, we'll need four of the product's digits behind the decimal point.

So instead of 3,096,375, the final product is actually 309.6375. Since we're dealing with dollars and cents, round the solution to the nearest cent: $309.64. The Hernandez family actually spent a total of $309.64 on gas during their road trip.

Multiplying Decimals

Try another example.

Let's say your math teacher wants to challenge you and asks for the product of 8.195 and 8.23.

That's a lot of digits behind those decimals! But, we know how to do this like clockwork now. Just follow the steps.

First, do normal multiplication: 8.23 times 8.195. Use the three in 8.23 and multiply it by 8.195. Then, multiply the 2 by 8.195 and the 8 by 8.195. Remember to follow the normal steps for multiplying multi-digit numbers.

Then count the total number of digits behind the decimal points in the original numbers. 8.195 has three digits after the decimal, and 8.23 has two digits after the decimal. The two numbers have a total of 5 digits after the decimal points. So our product needs to have five digits after the decimal, too. The final product is 67.44485.

Lesson Summary

To multiply decimals:

1. Multiply as usual, ignoring the decimals.

2. Determine the total number of digits behind the original numbers' decimal points.

3. Place the same number of digits behind the decimal point in the product.

There's really no difference between multiplication with whole numbers and decimal multiplication other than determining where the product's decimal should go. When determining where to place the decimal point in the product ask yourself… How many numbers are to the right of the decimal points?