Multiply Decimals
How do we multiply decimals using the standard algorithm?
📋 Standards & Objectives
- Multiply a whole number by a decimal using the standard algorithm
- Multiply a decimal by a decimal using the standard algorithm
- Place the decimal point correctly in the product by counting decimal places
- Handle zeros in the product when multiplying small decimals
🚀 Real-World Connection
🛒 Shopping Trip!
You want to buy 3 bags of trail mix that cost $4.75 each. How much will you spend?
You need to multiply a whole number by a decimal — 3 × $4.75
We multiply decimals every day — at the store, measuring for projects, cooking recipes. Today we'll learn a quick, reliable way to multiply any decimals using the standard algorithm.
📖 Vocabulary
A number that is multiplied by another number. In 3 × 4.75, both 3 and 4.75 are factors.
The answer when you multiply two or more factors. In 3 × 4.75 = 14.25, the product is 14.25.
The number of digits to the right of the decimal point. In 4.75, there are 2 decimal places (7 and 5).
A step-by-step method for multiplying. We'll multiply as if the decimals aren't there, then place the decimal in the product.
✨ Concept: Place the Decimal
The Big Idea for Multiplying Decimals
💡 The Key Insight
When we multiply decimals, we can ignore the decimal points, multiply as whole numbers, then count decimal places in the factors to place the decimal in the product.
Think of it as:
7 × 384 = 2,688
Then place the decimal:
7 × 3.84 = 26.88
← 2 decimal places in factors
📌 The 3-Step Rule
Multiplying Decimals with the Standard Algorithm
⚠️ Remember: If your product needs more decimal places than digits, add zeros in front! Example: 4 × 7 = 28, but 0.04 × 0.7 = 0.028 (3 decimal places needed!)
👁️ Problem 1
I Do — Watch MeIgnore the decimal — multiply 384 × 7 = 2688
3.84 has 2 decimal places
7 has 0 decimal places
Total: 2 decimal places
2688 → 26.88
Count 2 places from the right
👁️ Problem 2
I Do — Watch MeIgnore the decimal — multiply 297 × 5 = 1485
2.97 has 2 decimal places
5 has 0 decimal places
Total: 2 decimal places
1485 → 14.85
Count 2 places from the right
✍️ Problem 3
We Do — Together234 × 8 = 1872
23.4 has 1 decimal place
8 has 0 decimal places
Total: 1 decimal place
1872 → 187.2
Count 1 place from the right
✍️ Problem 4
We Do — Together823 × 6 = 4938
8.23 has 2 decimal places
6 has 0 decimal places
Total: 2 decimal places
4938 → 49.38
Count 2 places from the right
📝 Problem 5
You Do — Your Turn!Try this one on your own! Use the 3-step rule.
457 × 6 = 2742
4.57 has 2 decimal places
6 has 0 decimal places
Total: 2 decimal places
2742 → 27.42
📝 Problem 6
You Do — Your Turn!Try this one on your own! Use the 3-step rule.
1286 × 3 = 3858
12.86 has 2 decimal places
3 has 0 decimal places
Total: 2 decimal places
3858 → 38.58
✨ Decimal × Decimal
What changes when both factors have decimals?
💡 Same Rule — More Decimal Places!
When both factors have decimals, the same 3-step rule applies. The product will have more decimal places because you add up the decimal places from both factors.
Factor 1
5.2
1 decimal place
Factor 2
4.8
1 decimal place
Product
24.96
1 + 1 = 2 decimal places
📌 Updated Rule
Works for ANY decimal multiplication
💡 Tip for 2-digit × 2-digit: You'll need to multiply using partial products (just like whole-number multiplication with two-digit numbers). Line up your work carefully!
👁️ Problem 7
I Do — Watch Me52 × 48 = 2496
5.2 has 1 decimal place
4.8 has 1 decimal place
Total: 1 + 1 = 2 decimal places
2496 → 24.96
Count 2 places from the right
👁️ Problem 8
I Do — Watch Me53 × 24 = 1272
2.4 has 1 decimal place
5.3 has 1 decimal place
Total: 1 + 1 = 2 decimal places
1272 → 12.72
Count 2 places from the right
✍️ Problem 9
We Do — Together89 × 97 = 8633
8.9 has 1 decimal place
9.7 has 1 decimal place
Total: 1 + 1 = 2 decimal places
8633 → 86.33
Count 2 places from the right
✍️ Problem 10
We Do — Together264 × 51 = 13464
26.4 has 1 decimal place
5.1 has 1 decimal place
Total: 1 + 1 = 2 decimal places
13464 → 134.64
Count 2 places from the right
📝 Problem 11
You Do — Your Turn!Try this one on your own! Remember: both factors have decimals.
62 × 37 = 2294
3.7 has 1 decimal place
6.2 has 1 decimal place
Total: 1 + 1 = 2 decimal places
2294 → 22.94
📝 Problem 12
You Do — Your Turn!Try this one on your own! Use the 3-step rule.
145 × 28 = 4060
14.5 has 1 decimal place
2.8 has 1 decimal place
Total: 1 + 1 = 2 decimal places
4060 → 40.60
Count 2 places from the right
✨ Zeros in the Product
What happens when you need MORE decimal places than digits?
⚠️ Watch Out for This!
When multiplying small decimals like 0.04 × 0.7, the whole-number product might have fewer digits than the number of decimal places you need. You'll have to add zeros in front!
4 × 7 = 28
Whole number product
But we need 3 decimal places...
(0.04 has 2, 0.7 has 1)
28 → 0.028
Add a zero to make 3 places!
📌 Extended Rule
Handling zeros in the product
2 digits, need 3 places
28 → 0.028
2 digits, need 4 places
48 → 0.0048
1 digit, need 2 places
8 → 0.08
👁️ Problem 13
I Do — Watch Me4 × 7 = 28
Ignore the decimals and zeros — just multiply 4 × 7
0.04 has 2 decimal places
0.7 has 1 decimal place
Total: 2 + 1 = 3 decimal places
Product is 28 — that's only 2 digits, but we need 3 decimal places
28 → 0.028
Add a zero in front to make 3 decimal places!
👁️ Problem 14
I Do — Watch Me9 × 6 = 54
Just multiply 9 × 6
0.09 has 2 decimal places
0.6 has 1 decimal place
Total: 2 + 1 = 3 decimal places
Product is 54 — 2 digits, need 3 decimal places
54 → 0.054
Add a zero in front to make 3 decimal places!
✍️ Problem 15
We Do — Together5 × 8 = 40
Just multiply 5 × 8
0.05 has 2 decimal places
0.8 has 1 decimal place
Total: 2 + 1 = 3 decimal places
Product is 40 — 2 digits, need 3 decimal places
40 → 0.040 = 0.040
Add a zero in front to make 3 decimal places!
✍️ Problem 16
We Do — Together3 × 4 = 12
Just multiply 3 × 4
0.3 has 1 decimal place
0.04 has 2 decimal places
Total: 1 + 2 = 3 decimal places
Product is 12 — 2 digits, need 3 decimal places
12 → 0.012
Add a zero in front to make 3 decimal places!
📝 Problem 17
You Do — Your Turn!Watch out — you may need to add zeros!
6 × 3 = 18
0.06 has 2 decimal places
0.3 has 1 decimal place
Total: 2 + 1 = 3 decimal places
18 → 0.018
Add a zero to make 3 decimal places!
📝 Problem 18
You Do — Your Turn!Watch out — you may need to add zeros!
8 × 5 = 40
0.08 has 2 decimal places
0.5 has 1 decimal place
Total: 2 + 1 = 3 decimal places
40 → 0.040 = 0.040
Add a zero to make 3 decimal places!
🏆 Challenge Problem
Challenge — Multi-StepA snowman's head has a diameter of 0.75 feet. Its body has a diameter that is 2.4 times as large. What is the diameter of the snowman's body?
Body diameter = 0.75 × 2.4
Multiply as whole numbers: 75 × 24
0.75 → 2 places + 2.4 → 1 place = 3 places
1800 → 1.800 = 1.8
💬 Turn & Talk
Discuss with your partner
A student says: "When you multiply two numbers, the product is always bigger than either factor." Is this true for decimals? Can you think of an example where this is not true?
How do you know where to place the decimal point in the product? Explain the process to your partner in your own words.
📌 Key Takeaways
Multiply as whole numbers → Count decimal places in both factors → Place the decimal in the product.
Add up the decimal places from all factors. That's how many decimal places the product must have.
If you need more decimal places than digits, add zeros in front. Example: 28 with 3 decimal places → 0.028
Always check if your answer makes sense! Round the factors to estimate, then compare. If 5.2 × 4.8 ≈ 5 × 5 = 25, then 24.96 makes sense.
🎫 Exit Ticket
Show what you know! Solve on your exit ticket paper.
9 × 5.63
4.3 × 7.6
0.07 × 0.4
Great Work Today!
You learned how to multiply decimals using the standard algorithm — whole numbers × decimals, decimal × decimal, and even tricky zeros in the product!
Remember: Multiply → Count → Place!
Keep practicing — you've got this! 💪