By Mark Zegarelli

To multiply two decimals, don’t worry about lining up the decimal points. In fact, to start out, ignore the decimal points. Here’s how the multiplication works:

  1. Perform the multiplication just as you would for whole numbers.

  2. When you’re done, count the number of digits to the right of the decimal point in each factor and add the results.

  3. Place the decimal point in your answer so that your answer has the same number of digits after the decimal point.

Even if the last digit in the answer is 0, you still need to count this as a digit when placing the decimal point in a multiplication problem. After the decimal point is in place, however, you can drop trailing zeros.

Sample question

  1. Multiply the following decimals: 74.2 x 0.35 = ?

    25.97. Ignoring the decimal points, perform the multiplication just as you would for whole numbers:

    image0.jpg

    At this point, you’re ready to find out where the decimal point goes in the answer. Count the number of decimal places in the two factors (74.2 and 0.35), add these two numbers together (1 + 2 = 3), and place the decimal point in the answer so that it has three digits to the right of the decimal point:

    image1.jpg

Practice questions

  1. Multiply these decimals: 0.635 x 0.42 = ?

  2. Perform the following decimal multiplication: 0.675 x 34.8 = ?

  3. Solve the following multiplication problem: 943 x 0.0012 = ?

  4. Find the solution to this decimal multiplication: 1.006 x 0.0807 = ?

Following are answers to the practice questions:

  1. 0.635 x 0.42 = 0.2667. Place the first number on top of the second number, ignoring the decimal points. Complete the multiplication as you would for whole numbers:

    image2.jpg

    At this point, you’re ready to find out where the decimal point goes in the answer. Count the number of decimal places in the two factors, add these two numbers together (3 + 2 = 5), and place the decimal point in the answer so that it has five digits after the decimal point. After you place the decimal point (but not before!), you can drop the trailing zero.

  2. 0.675 x 34.8 = 23.49. Ignore the decimal points and simply place the first number on top of the second. Complete the multiplication as you would for whole numbers:

    image3.jpg

    Count the number of decimal places in the two factors, add these two numbers together (3 + 1 = 4), and place the decimal point in the answer so that it has four digits after the decimal point. Last, you can drop the trailing zeros.

  3. 943 x 0.0012 = 1.1316. Complete the multiplication as you would for whole numbers:

    image4.jpg

    Zero digits come after the decimal point in the first factor, and you have four after-decimal digits in the second factor, for a total of 4 (0 + 4 = 4); place the decimal point in the answer so that it has four digits after the decimal point.

  4. 1.006 x 0.0807 = 0.0811842. Complete the multiplication as you would for whole numbers:

    image5.jpg

    You have a total of seven digits after the decimal points in the two factors — three in the first factor and four in the second (3 + 4 = 7) — so place the decimal point in the answer so that it has seven digits after the decimal point. Notice that you need to create an extra decimal place in this case by attaching an additional nontrailing 0.