6.5 Multiplication of decimals

Section overview

• The Logic Behind the Method
• The Method of Multiplying Decimals
• Calculators
• Multiplying Decimals By Powers of 10
• Multiplication in Terms of “Of”

The logic behind the method

Consider the product of 3.2 and 1.46. Changing each decimal to a fraction, we have

$\begin{array}{ccc}(3\text{.}2)(1\text{.}\text{46})& =& 3\frac{2}{\text{10}}\cdot 1\frac{\text{46}}{\text{100}}\hfill \\ & =& \frac{\text{32}}{\text{10}}\cdot \frac{\text{146}}{\text{100}}\hfill \\ & =& \frac{\text{32}\cdot \text{146}}{\text{10}\cdot \text{100}}\hfill \\ & =& \frac{\text{4672}}{\text{1000}}\hfill \\ & =& 4\frac{\text{672}}{\text{1000}}\hfill \\ & =& \text{four and six hundred seventy-two thousandths}\\ & =& \text{4}\text{.}\text{672}\hfill \end{array}$

Thus, $(3\text{.}2)(1\text{.}\text{46})=\text{4}\text{.}\text{672}$ .

Notice that the factor

$\left(\begin{array}{}\text{3.2 has 1 decimal place,}\\ \text{1.46 has 2 decimal places,}\\ \text{and the product}\\ \text{4.672 has 3 decimal places.}\end{array}\right\}1+2=3$

Using this observation, we can suggest that the sum of the number of decimal places in the factors equals the number of decimal places in the product.

The method of multiplying decimals

Method of multiplying decimals

1. Multiply the numbers as if they were whole numbers.
2. Find the sum of the number of decimal places in the factors.
3. The number of decimal places in the product is the sum found in step 2.

Sample set a

Find the following products.

Practice set a

Find the following products.

Calculators

Calculators can be used to find products of decimal numbers. However, a calculator that has only an eight-digit display may not be able to handle numbers or products that result in more than eight digits. But there are plenty of inexpensive ($50 - $75) calculators with more than eight-digit displays.

Sample set b

Find the following products, if possible, using a calculator.