Multiplying Decimals

For Elementary Students

The Secret: Ignore the Decimal at First!

Multiplying decimals is easier than you think!

Think about it like this: First multiply like they're whole numbers, then put the decimal point back at the end!

The Three Steps

Step 1: Ignore the decimals — multiply like whole numbers
Step 2: Count the decimal places in BOTH numbers
Step 3: Put the decimal in your answer (same total places)

Let's Try: 1.2 × 0.3

Step 1: Ignore the decimals

1.2 → 12
0.3 → 3
Multiply: 12 × 3 = 36

Step 2: Count decimal places

1.2 has 1 decimal place (one digit after the dot)
0.3 has 1 decimal place
Total: 1 + 1 = 2 decimal places

Step 3: Put the decimal in 36 so it has 2 decimal places

36 → 0.36
(count 2 places from the right)

Answer: 1.2 × 0.3 = 0.36

Another Example: 2.5 × 4

Step 1: Ignore decimals: 25 × 4 = 100

Step 2: Count decimal places:

• 2.5 has 1 place
• 4 has 0 places (it's a whole number!)
• Total: 1 place

Step 3: Put decimal: 100 → 10.0 (1 place from right)

Answer: 2.5 × 4 = 10

Quick Trick: Multiplying by 10, 100, 1000

Super easy shortcut!

Multiply by 10: Move the decimal point 1 place right

3.45 × 10 = 34.5

Multiply by 100: Move it 2 places right

0.07 × 100 = 7 (or 7.0)

Multiply by 1000: Move it 3 places right

1.2 × 1000 = 1200

Memory trick: Count the zeros! 10 has 1 zero, move 1 place. 100 has 2 zeros, move 2 places!

Where the Decimal Goes

Example: 3.4 × 2.5

Multiply: 34 × 25 = 850

Count decimal places: 1 + 1 = 2 places

Put decimal 2 places from the right:

850 → 8.50 → 8.5

Answer: 8.5

For Junior High Students

The Method

Multiplying decimals is almost the same as multiplying whole numbers. You just need to handle the decimal point at the end.

Three-step process:

1. Ignore the decimal points — Multiply as if both numbers were whole numbers
2. Count decimal places — Count the total number of decimal places in both original numbers
3. Place the decimal point — Put the decimal point in the answer so it has the same total number of decimal places

Why it works: This method accounts for the fact that multiplying by a decimal is like multiplying then dividing by powers of 10.

Worked Example: 1.2 × 0.3

Step 1: Ignore decimals: 12 × 3 = 36

Step 2: Count decimal places:

• 1.2 has 1 decimal place
• 0.3 has 1 decimal place
• Total = 2 decimal places

Step 3: Place the decimal: 36 → 0.36 (2 places from right)

Answer: 0.36

Verification: 1.2 × 0.3 = (12/10) × (3/10) = 36/100 = 0.36 ✓

Worked Example: 2.5 × 4.12

Step 1: Ignore decimals: 25 × 412 = 10,300

Step 2: Count decimal places:

• 2.5 has 1 place
• 4.12 has 2 places
• Total = 3 places

Step 3: Place the decimal: 10300 → 10.300 → 10.3

Answer: 10.3

Note: You can remove trailing zeros after the decimal point: 10.300 = 10.3

Worked Example: 0.04 × 0.5

Step 1: Ignore decimals: 4 × 5 = 20

Step 2: Count decimal places:

• 0.04 has 2 places
• 0.5 has 1 place
• Total = 3 places

Step 3: Place the decimal: 20 → need 3 places → 0.020 → 0.02

Answer: 0.02

Important: When you need more decimal places than you have digits, add zeros on the left!

Multiplying by 10, 100, 1000

These are shortcuts worth memorizing:

Multiply by 10: Move the decimal point 1 place right

3.45 × 10 = 34.5

Multiply by 100: Move it 2 places right

0.07 × 100 = 7.00 = 7

Multiply by 1000: Move it 3 places right

1.2 × 1000 = 1200.0 = 1200

General rule: Multiplying by 10^n moves the decimal point n places to the right.

Why it works: Each factor of 10 increases the place value of each digit by one position.

Multiplying by 0.1, 0.01, 0.001

Multiplying by decimals less than 1 moves the decimal left:

Multiply by 0.1 (divide by 10): Move decimal 1 place left

45 × 0.1 = 4.5

Multiply by 0.01 (divide by 100): Move decimal 2 places left

45 × 0.01 = 0.45

Multiply by 0.001 (divide by 1000): Move decimal 3 places left

45 × 0.001 = 0.045

Key insight: Multiplying by 0.1 is the same as dividing by 10!

Estimating to Check Answers

Estimating helps catch mistakes. Round to whole numbers first to check if your answer makes sense.

Example: 1.2 × 0.3

Estimate: Round to 1 × 0 or 1 × 1/2 ≈ 0.5

Actual: 0.36 (close to 0.5!) ✓

Example: 4.8 × 3.2

Estimate: Round to 5 × 3 = 15

Actual: Let's calculate

• Ignore decimals: 48 × 32 = 1536
• Decimal places: 1 + 1 = 2
• Place decimal: 15.36

Check: 15.36 is close to 15! ✓

Real-Life Applications

Shopping: "Each item costs $2.50. Buy 3.5 pounds"

$2.50 × 3.5
= 250 × 35 ÷ 100 (2 decimal places total)
= 8750 ÷ 100
= $8.75

Measurements: "A board is 1.5 meters long. Need 2.4 times that length"

1.5 × 2.4 = 3.6 meters

Conversion: "1 inch = 2.54 cm. Convert 5.5 inches to cm"

5.5 × 2.54
= 55 × 254 ÷ 100 (2 decimal places)
= 13970 ÷ 100
= 13.97 cm

Common Mistakes

Mistake 1: Forgetting to count decimal places

❌ 1.2 × 0.3 = 36 (forgot to place decimal!) ✓ 1.2 × 0.3 = 0.36

Mistake 2: Counting decimal places wrong

❌ 0.04 has 1 decimal place (wrong — it has 2!) ✓ Count from the decimal point: 0.04 = 2 places

Mistake 3: Not adding zeros when needed

❌ 4 × 5 = 20 with 3 decimal places → 0.2 (wrong!) ✓ Need 3 places: 0.020 = 0.02

Multiplying by Powers of 10: Pattern

Moving right (multiply):

3.45 × 10 = 34.5
3.45 × 100 = 345
3.45 × 1000 = 3450

Moving left (multiply by decimals):

3.45 × 0.1 = 0.345
3.45 × 0.01 = 0.0345
3.45 × 0.001 = 0.00345

Memory aid: Bigger multiplier → decimal moves right. Smaller multiplier → decimal moves left.

Mental Math Strategies

Doubling: 2.5 × 4 Think: 2.5 × 2 = 5, then 5 × 2 = 10

Halving: 6 × 0.5 Think: half of 6 = 3

Breaking apart: 3.5 × 4

• 3 × 4 = 12
• 0.5 × 4 = 2
• 12 + 2 = 14

Tips for Success

Tip 1: Always estimate first to check if your answer is reasonable

Tip 2: Count decimal places carefully — count digits after the decimal point

Tip 3: Remember: multiplying makes numbers bigger (unless multiplying by something less than 1)

Tip 4: For powers of 10, just move the decimal point — no multiplication needed!

Tip 5: Remove unnecessary trailing zeros: 5.0 = 5 and 0.30 = 0.3

Practice