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Multiply decimal numbers
Learn step-by-step with practice exercises built right in.
We multiply decimals for real-world situations:
When multiplying decimals:
Example: 3.2 × 1.5
Multiply: 0.4 × 3 = ?
Step 1: Multiply ignoring the decimal 4 × 3 = 12
Step 2: Count decimal places 0.4 has 1 decimal place 3 has 0 decimal places Total: 1 decimal place
Step 3: Put decimal in answer 12 → 1.2
Answer: 1.2 ✓
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Step 1: Multiply as if they were whole numbers
Step 2: Count decimal places
Step 3: Put decimal point in answer
Example: 4.56 × 3
Step 1: Multiply like whole numbers
Step 2: Count decimal places
Step 3: Place the decimal
Quick rule: Move the decimal point to the RIGHT!
Multiply by 10: Move decimal 1 place right
Multiply by 100: Move decimal 2 places right
Multiply by 1,000: Move decimal 3 places right
Why? Each zero adds one place value!
Example: 0.3 × 0.4
Step 1: Multiply like whole numbers
Step 2: Count decimal places
Step 3: Place decimal (might need extra zeros!)
Important: When multiplying numbers less than 1, the answer is SMALLER than both numbers!
Example: You buy 3 notebooks for $2.75 each. How much total?
Solve: 3 × $2.75
Step 1: Multiply
Step 2: Count decimals
Step 3: Place decimal
Check: Does 3 = $9 ✓
Before multiplying, estimate:
Example: 4.8 × 3.2 ≈ ?
Actual calculation: 4.8 × 3.2 = 15.36 ✓ (Close to 15!)
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 ✓
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 ✓
Gas prices: 12.5 gallons × $3.89 per gallon
Recipe scaling: Recipe calls for 2.5 cups flour. You're making 1.5 times the recipe
Steps to remember:
Check your work:
❌ 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
Multiplying by 0.1, 0.01, 0.001: Move decimal to the LEFT!
Zero in the product:
Multiply: 3.2 × 4
Step 1: Ignore the decimal and multiply 32 × 4 = 128
Step 2: Count decimal places in the original problem 3.2 has 1 decimal place 4 has 0 decimal places Total: 1 decimal place
Step 3: Place the decimal in the answer 128 → 12.8 (1 decimal place)
Answer: 12.8
Multiply: 2.5 × 4 = ?
Step 1: Ignore decimals and multiply 25 × 4 = 100
Step 2: Count decimal places 2.5 has 1 decimal place 4 has 0 decimal places Total: 1 decimal place
Step 3: Place the decimal 100 → 10.0 = 10
Answer: 10 ✓
Calculate: 0.5 × 0.6
Step 1: Multiply without decimals 5 × 6 = 30
Step 2: Count total decimal places 0.5 has 1 decimal place 0.6 has 1 decimal place Total: 1 + 1 = 2 decimal places
Step 3: Place the decimal 30 → 0.30 = 0.3 (2 decimal places from the right)
Answer: 0.3
Multiply: 1.2 × 0.5 = ?
Step 1: Multiply without decimals 12 × 5 = 60
Step 2: Count decimal places 1.2 has 1 decimal place 0.5 has 1 decimal place Total: 2 decimal places
Step 3: Place decimal 60 → 0.60 = 0.6
Answer: 0.6 ✓
A book costs $12.50. How much do 3 books cost?
Multiply: 12.50 × 3
Step 1: Multiply without the decimal 1250 × 3 = 3750
Step 2: Count decimal places 12.50 has 2 decimal places 3 has 0 decimal places Total: 2 decimal places
Step 3: Place the decimal 3750 → 37.50
Answer: $37.50
Multiply: 2.4 × 1.5
Step 1: Multiply without decimals 24 × 15 = 360
Step 2: Count decimal places 2.4 has 1 decimal place 1.5 has 1 decimal place Total: 1 + 1 = 2 decimal places
Step 3: Place the decimal 360 → 3.60 = 3.6
Answer: 3.6
A pencil costs $0.75. How much do 6 pencils cost?
Multiply: 0.75 × 6
Step 1: Multiply ignoring decimal 75 × 6 = 450
Step 2: Count decimal places 0.75 has 2 decimal places 6 has 0 decimal places Total: 2 decimal places
Step 3: Place decimal 450 → 4.50
Answer: $4.50 ✓
6 pencils cost $4.50!
Multiply: 3.25 × 2.4 = ?
7800
Step 2: Count decimal places 3.25 has 2 decimal places 2.4 has 1 decimal place Total: 3 decimal places
Step 3: Place decimal 7800 → 7.800 = 7.8
Answer: 7.8 ✓
A rectangle has length 4.5 cm and width 2.8 cm. What is the area?
Area = length × width Area = 4.5 × 2.8
Step 1: Multiply without decimals 45 × 28 = 1260
Break it down: 45 × 28 = 45 × 20 + 45 × 8 = 900 + 360 = 1260
Step 2: Count decimal places 4.5 has 1 decimal place 2.8 has 1 decimal place Total: 2 decimal places
Step 3: Place the decimal 1260 → 12.60 = 12.6
Answer: 12.6 square cm