Lesson 39: Multiplying Decimal Numbers

New Concept

To multiply decimal numbers, first multiply as if they were whole numbers. Then, count the total decimal places in the factors to place the decimal.

When we multiply decimal numbers, the product has the same number of decimal places as there are in all of the factors combined.

What’s next

This card introduces the core rule. Next, you'll apply it through worked examples, including squaring decimals and solving real-world word problems.

Property

One way to multiply decimal numbers is to write each decimal number as a proper fraction and then multiply the fractions.

Examples

$0.6 \times 0.4 = \frac{6}{10} \times \frac{4}{10} = \frac{24}{100} = 0.24$
$0.25 \times 0.2 = \frac{25}{100} \times \frac{2}{10} = \frac{50}{1000} = 0.050$
$1.5 \times 0.3 = \frac{15}{10} \times \frac{3}{10} = \frac{45}{100} = 0.45$

Explanation

Turning decimals into fractions makes multiplication easy to understand. Just multiply the top numbers (numerators) and the bottom numbers (denominators). The final fraction's denominator, a power of 10, reveals exactly how many decimal places your final answer needs. It’s a foolproof way to see where the decimal point goes!

Property

When we multiply decimal numbers, the product has the same number of decimal places as there are in all of the factors combined.

Examples

$0.25 \text{ (2 places)} \times 0.7 \text{ (1 place)} = 0.175 \text{ (3 places total)}$
$1.6 \text{ (1 place)} \times 3 \text{ (0 places)} = 4.8 \text{ (1 place total)}$
$0.04 \text{ (2 places)} \times 0.02 \text{ (2 places)} = 0.0008 \text{ (4 places total)}$

Explanation

Forget the decimal points and multiply the numbers like they're whole. After you have the product, count the total number of decimal places in your original factors. Now, place the decimal point in your answer so it has that same number of places. It's the ultimate shortcut for decimal multiplication!

Property

To square a decimal, you multiply the number by itself. For example, $(2.5)^2$ means you calculate $2.5 \times 2.5$.

Examples

$(0.8)^2 = 0.8 \text{ (1 place)} \times 0.8 \text{ (1 place)} = 0.64 \text{ (2 places)}$
$(1.2)^2 = 1.2 \text{ (1 place)} \times 1.2 \text{ (1 place)} = 1.44 \text{ (2 places)}$
$(0.05)^2 = 0.05 \text{ (2 places)} \times 0.05 \text{ (2 places)} = 0.0025 \text{ (4 places)}$

Explanation

Squaring a decimal is just a special case of multiplying! You multiply the number by itself. Use the same counting rule: multiply as if they were whole numbers, then count up the total decimal places from both identical factors. Place the decimal point accordingly. This trick works every single time for any squared decimal!