Multiplying Decimals

What You’ll Learn

In this lesson you’ll learn how to multiply decimals by ignoring the point first, then placing the decimal correctly in the answer.

The Concept

Multiplying decimals: First multiply as if they were whole numbers, then count the total decimal places in both factors and place that many in the product.

Example: $1.2 \times 0.3$

1. Ignore decimals and multiply $12 \times 3$:

$$\begin{array}{rr} 1 & 2 \\ \times & 3 \\ \hline 3 & 6 \end{array}$$

2. Total decimal places: 1 (from 1.2) + 1 (from 0.3) = 2
3. Place decimal 2 places from right: $0.36$

Another: $2.5 \times 4 = 10.0$ (2.5 has 1 place, 4 has 0 → 1 place in the answer)

Worked Examples

Multiply $3.4 \times 0.25$

1. Ignore decimals and multiply $34 \times 25$:

$$\begin{array}{rrrr} & & \scriptsize{2} & \\ & & 3 & 4 \\ \times & & 2 & 5 \\ \hline & 1 & 7 & 0 \\ & 6 & 8 & 0 \\ \hline & 8 & 5 & 0 \end{array}$$

2. Total places: 1 (from 3.4) + 2 (from 0.25) = 3
3. Place decimal 3 from right: $0.850 → 0.85$

Multiply $1.6 \times 2.5$

1. Ignore decimals and multiply $16 \times 25$:

$$\begin{array}{rrr} & \scriptsize{3} & \\ & 1 & 6 \\ \times & 2 & 5 \\ \hline & 8 & 0 \\ 3 & 2 & 0 \\ \hline 4 & 0 & 0 \end{array}$$

2. Places: 1 + 1 = 2
3. Place decimal: $4.00 → 4$

Real-World Applications

Multiplying decimals calculates costs (2.5 hours × 18.50 dollars/hour = 46.25 dollars), area (room 12.5 ft × 10.75 ft), or sales tax (subtotal 89.99 dollars × 0.08 tax rate = 7.20 dollars tax). It’s essential for budgeting or shopping.

You’ve Got This

The trick is to multiply normally and then slide the decimal. Count the places carefully. Practice with money (like tips or tax) and always estimate first ($2.5 \times 18 \approx 45$). You’ll avoid mistakes quickly.

Quiz

What is 0.4 × 0.5?

• A.0.20
• B.2.0
• C.0.09
• D.0.45

Multiply 1.25 × 6.

• A.7.50
• B.7.25
• C.7.00
• D.8.50

A part costs 3.75 dollars. For 4 of them, total?

• A.15.00 dollars
• B.15.50 dollars
• C.14.00 dollars
• D.14.75 dollars

What is 2.3 × 1.4?

• A.3.22
• B.3.12
• C.3.32
• D.2.22

What is 0.12 × 0.3?

• A.0.036
• B.0.36
• C.3.6
• D.0.0036