ASVAB Preparation: How to Multiply and Divide Decimals

By Rod Powers

The ASVAB contains two math subtests. You will inevitably encounter decimals so make sure you are prepared and know how to multiply and divide decimals and as well as perform other operations when necessary.

Multiplying decimals

Multiplying decimals requires three steps:

  1. Convert the decimals to whole numbers by moving the decimal points to the right, remembering to count how many spaces you move each decimal point.

  2. Multiply the whole numbers just as you’d perform any other multiplication.

  3. Place the decimal point in the product by moving the decimal point to the left the same number of total spaces you moved the decimal points to the right at the beginning.

Multiply: 3.724 × 0.0004 × 9.42.

First convert the decimals to whole numbers by moving the decimal points to the right (remember to count).

3.724 becomes 3,724 (decimal moved three spaces).

0.0004 becomes 4 (decimal moved four spaces).

9.42 becomes 942 (decimal moved two spaces).

Next, perform the multiplication on the whole numbers:

3,724 × 4 × 942 = 14,032,032

Finally, replace the decimal point in the correct position by moving it to the left the same number of places you moved the points to the right. You moved the decimal points a total of nine spaces to the right at the beginning, so now place the decimal point nine spaces to the left:

14,032,032 becomes 0.014032032

If you run out of numbers before you’re finished counting spaces to the left, add zeros (as shown in the example) until you’re finished counting.

Dividing decimals

Dividing decimals can be a challenge. You have to use both subtraction and multiplication. You also need to be pretty good at rounding and estimating numbers.

You’re not allowed to use a calculator on the ASVAB math subtests.

You can divide decimals in two ways: long division and conversion.

Method 1: Long division

To do long division with decimals, follow these steps:

  1. If the divisor isn’t a whole number, move the decimal point in the divisor all the way to the right (to make it a whole number), and move the decimal point in the dividend the same number of places to the right.

  2. Position the decimal point in the result directly above the decimal point in the dividend.

  3. Divide as usual.

    If the divisor doesn’t go into the dividend evenly, add zeros to the right of the last digit in the dividend and keep dividing until it comes out evenly or a repeating pattern shows up.

Try the following division problem:

7.42 ÷ 0.7

Write the problem on your scratch paper in long-division form:

image0.jpg

Now move the decimal point one place to the right, which makes the divisor a whole number. Also move the decimal point in the dividend one place to the right:

image1.jpg

Position the decimal point in the result directly above the decimal point in the dividend:

image2.jpg

Divide as usual. Seven goes into 70 ten times with 4 leftover; then drop the 2 down:

image3.jpg

Seven goes into 42 six times:

image4.jpg

When you’re finished dividing decimals, you’re finished. You don’t have to move the decimal around like you do after you’ve multiplied decimals.

Method 2: Conversion

The other way to divide decimals is to convert the decimals to fractions, and then divide the fractions.

Try the problem above, using the conversion method.

7.42 ÷ 0.7

First, convert the decimals to fractions:

image5.jpg

You should be able to do the smaller decimals more quickly.

image6.jpg

With some practice, this can all become mental math.

image7.jpg

Take the reciprocal of the divisor (flip the second fraction upside down) and then multiply:

image8.jpg

The fraction

image9.jpg

can be simplified to

image10.jpg

Convert 3/5 to a decimal, and the answer is 10.6.