Multiplying Decimals

Why Multiply Decimals?

We multiply decimals for real-world situations:

• Money: 4 items cost $2.50 each → 4 ×$2.50
• Measurements: 3.5 yards of fabric times 2
• Recipes: Making 1.5 times a recipe

The Basic Rule

When multiplying decimals:

1. Ignore the decimal points and multiply like whole numbers
2. Count the total decimal places in BOTH numbers
3. Put that many decimal places in your answer

Step-by-Step Process

Example: 3.2 × 1.5

Step 1: Multiply as if they were whole numbers

• 32 × 15 = 480

Step 2: Count decimal places

• 3.2 has 1 decimal place
• 1.5 has 1 decimal place
• Total: 1 + 1 = 2 decimal places

Step 3: Put decimal point in answer

• Start from the right
• Count 2 places to the left
• 480 → 4.80 = 4.8 ✓

Multiplying by Whole Numbers

Example: 4.56 × 3

Step 1: Multiply like whole numbers

• 456 × 3 = 1,368

Step 2: Count decimal places

• 4.56 has 2 decimal places
• 3 has 0 decimal places
• Total: 2 decimal places

Step 3: Place the decimal

• 1,368 → 13.68 ✓

Multiplying by 10, 100, 1,000

Quick rule: Move the decimal point to the RIGHT!

Multiply by 10: Move decimal 1 place right

• 3.45 × 10 = 34.5

Multiply by 100: Move decimal 2 places right

• 3.45 × 100 = 345

Multiply by 1,000: Move decimal 3 places right

• 3.45 × 1,000 = 3,450

Why? Each zero adds one place value!

Multiplying Decimals Less Than 1

Example: 0.3 × 0.4

Step 1: Multiply like whole numbers

• 3 × 4 = 12

Step 2: Count decimal places

• 0.3 has 1 decimal place
• 0.4 has 1 decimal place
• Total: 2 decimal places

Step 3: Place decimal (might need extra zeros!)

• 12 → 0.12 ✓

Important: When multiplying numbers less than 1, the answer is SMALLER than both numbers!

Money Problems

Example: You buy 3 notebooks for $2.75 each. How much total?

Solve: 3 × $2.75

Step 1: Multiply

• 3 × 275 = 825

Step 2: Count decimals

• 2.75 has 2 decimal places
• Total: 2 decimal places

Step 3: Place decimal

• 825 → $8.25 ✓

Check: Does $8.25 make sense? Yes! About 3 ×$3 = $9 ✓

Estimation to Check Your Work

Before multiplying, estimate:

Example: 4.8 × 3.2 ≈ ?

• Round: 5 × 3 = 15
• So answer should be close to 15

Actual calculation: 4.8 × 3.2 = 15.36 ✓ (Close to 15!)

Partial Products Method

Example: 2.4 × 1.3

Break into parts:

    2.4
  × 1.3
  -----
    0.12  (0.4 × 0.3)
    0.60  (2.0 × 0.3)
    0.40  (0.4 × 1.0)
  + 2.00  (2.0 × 1.0)
  -----
    3.12 ✓

Array/Area Model

Visual way to multiply: 2.3 × 1.4

        2    +    0.3
    ____________
1   |  2    |  0.3   |  = 2.3
    |_______|________|
0.4 |  0.8  |  0.12  |  = 0.92
    |_______|________|
    = 2.8   = 0.42

Add all sections: 2 + 0.3 + 0.8 + 0.12 = 3.22 ✓

Real-World Applications

Gas prices: 12.5 gallons × $3.89 per gallon

• 125 × 389 = 48,625
• 3 total decimal places
• $48.625 →$48.63 (round to cents) ✓

Recipe scaling: Recipe calls for 2.5 cups flour. You're making 1.5 times the recipe

• 2.5 × 1.5 = 3.75 cups ✓

Practice Tips

Steps to remember:

1. Multiply like whole numbers (ignore decimals)
2. Count total decimal places in problem
3. Count that many places from right in answer
4. Add zeros if needed at the front

Check your work:

• Estimate first
• Does the decimal placement make sense?
• Is the answer reasonable for the problem?

Common Mistakes

❌ Forgetting to count decimal places ❌ Counting decimal places in the answer instead of the problem ❌ Putting decimal in the wrong place ❌ Not adding leading zeros when needed (like 0.12)

✅ Always count decimals in BOTH original numbers ✅ Start from the right and count left ✅ Estimate to check if your answer is reasonable ✅ Add zeros in front if you need more decimal places

Special Cases

Multiplying by 0.1, 0.01, 0.001: Move decimal to the LEFT!

• 45.6 × 0.1 = 4.56 (move 1 left)
• 45.6 × 0.01 = 0.456 (move 2 left)
• 45.6 × 0.001 = 0.0456 (move 3 left)

Zero in the product:

• 0.5 × 0.2 = 0.10 = 0.1 (can drop final zero)
• But keep zeros between digits: 0.05 × 2 = 0.10 ✓