Tutorial: How to Multiply Decimals

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🎯 What You Will Learn

In this tutorial, you will learn how to multiply decimals step by step. By the end, you'll be able to:

✅ Multiply a decimal by a whole number
✅ Multiply a decimal by another decimal
✅ Multiply by 10, 100, and 1,000
✅ Know where to place the decimal point in the answer

🔑 The Big Idea

Multiplying decimals is just like multiplying whole numbers — the only extra step is figuring out where the decimal point goes in the answer.

📘 Part 1: Decimal × Whole Number

When you multiply a decimal by a whole number, follow these three steps:

3-Step Method

Step 1: Ignore the decimal point and multiply as whole numbers.
Step 2: Count the total decimal places in the original numbers.
Step 3: Place the decimal point in the answer so it has that many decimal places.

✏️ Worked Example A — Tenths × Whole

1 Problem: 2.4 × 3

2 Ignore the decimal — multiply 24 × 3 = 72

3 2.4 has 1 decimal place. So put 1 decimal place in the answer.

✅ Answer: 2.4 × 3 = 7.2

✏️ Worked Example B — Hundredths × Whole

1 Problem: 1.25 × 4

2 Ignore the decimal — multiply 125 × 4 = 500

3 1.25 has 2 decimal places. So put 2 decimal places in the answer.

✅ Answer: 1.25 × 4 = 5.00

💡 Tip: A whole number has 0 decimal places. So in 2.4 × 3, you only count the 1 decimal place from 2.4.

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📐 How It Looks Vertically — set it up like long multiplication

Example: 3.6 × 4

3.6

× 4

14.4

↑ 1 decimal place

Example: 5.24 × 3

5.24

× 3

15.72

↑ 2 decimal places

Example: 0.08 × 7

0.08

× 7

0.56

↑ 2 decimal places

✍️ Try It Yourself — Decimal × Whole Number

0.7 × 5 =

3.2 × 4 =

1.05 × 6 =

4.8 × 3 =

0.25 × 8 =

6.15 × 2 =

📗 Part 2: Decimal × Decimal (Tenths × Tenths)

When both numbers have decimals, the method is the same — but you count the decimal places in both numbers and add them together.

🔑 Key Rule

Total decimal places in the answer = decimal places in the first number + decimal places in the second number.

Example: 0.3 × 0.4 → 1 place + 1 place = 2 decimal places in the answer.

✏️ Worked Example C — Tenths × Tenths

1 Problem: 0.6 × 0.3

2 Ignore the decimals — multiply 6 × 3 = 18

3 Count: 0.6 has 1 place + 0.3 has 1 place = 2 places total

4 Place the decimal: 18 → 0.18

✅ Answer: 0.6 × 0.3 = 0.18

✏️ Worked Example D — Larger Tenths

1 Problem: 1.2 × 3.4

2 Ignore the decimals — multiply 12 × 34 = 408

3 Count: 1.2 has 1 place + 3.4 has 1 place = 2 places total

4 Place the decimal: 408 → 4.08

✅ Answer: 1.2 × 3.4 = 4.08

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📕 Part 3: Multiplying with Hundredths

Hundredths have 2 decimal places. When you multiply hundredths by tenths, the answer can have 3 or even 4 decimal places!

✏️ Worked Example E — Hundredths × Whole

1 Problem: 0.15 × 6

2 Multiply: 15 × 6 = 90

3 0.15 has 2 places + whole number has 0 = 2 places

4 Place the decimal: 90 → 0.90

✅ Answer: 0.15 × 6 = 0.90

✏️ Worked Example F — Hundredths × Tenths

1 Problem: 0.25 × 0.4

2 Multiply: 25 × 4 = 100

3 0.25 has 2 places + 0.4 has 1 place = 3 places

4 Place the decimal: 100 → 0.100

✅ Answer: 0.25 × 0.4 = 0.100 = 0.1

⚠️ Remember: You may need to add a leading zero if the product doesn't have enough digits. For example, if you need 3 decimal places but the product is only 2 digits (like 12), write it as 0.012.

✍️ Try It Yourself — Decimal × Decimal

0.4 × 0.5 =

1.3 × 2.1 =

0.12 × 5 =

0.7 × 0.9 =

2.5 × 1.4 =

0.35 × 0.2 =

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⚡ Part 4: Multiply by 10, 100, and 1,000

Multiplying by powers of 10 is the easiest kind of decimal multiplication. You just move the decimal point to the right!

🔑 Power-of-10 Shortcut

× 10 → move the decimal point 1 place to the right
× 100 → move the decimal point 2 places to the right
× 1,000 → move the decimal point 3 places to the right

Example G

3.45 × 10

Move decimal 1 place right →

= 34.5

Example H

3.45 × 100

Move decimal 2 places right →

= 345

Example I

3.45 × 1,000

Move decimal 3 places right →

= 3,450

💡 Tip: Count the zeros in 10, 100, or 1,000 — that tells you how many places to move! 10 has 1 zero, 100 has 2, 1,000 has 3.

✏️ Worked Example L — When You Run Out of Digits

1 Problem: 2.3 × 1,000

2 The rule says move the decimal 3 places right, but 2.3 only has 1 digit after the point.

3 Add placeholder zeros so there's room to move: 2.300

4 Move the decimal 3 places right → 2,300

✅ Answer: 2.3 × 1,000 = 2,300

✍️ Try It Yourself — Powers of 10

2.7 × 10 =

0.45 × 100 =

1.306 × 1,000 =

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🧠 Part 5: Using Estimation to Check Your Answer

Always estimate first to make sure your decimal point is in the right place. Round each decimal to the nearest whole number, then multiply.

✏️ Worked Example J — Estimate & Check

1 Problem: 4.8 × 3.2

2 Estimate: Round 4.8 → 5 and 3.2 → 3, so about 5 × 3 = 15

3 Exact: 48 × 32 = 1,536. Need 2 decimal places → 15.36

4 Check: 15.36 is close to our estimate of 15 ✓

✅ Answer: 4.8 × 3.2 = 15.36

✏️ Worked Example K — Catching a Mistake

1 Problem: 6.3 × 2.9

2 Estimate: Round 6.3 → 6 and 2.9 → 3, so about 6 × 3 = 18

3 Exact: 63 × 29 = 1,827. Need 2 decimal places → 18.27

4 Check: 18.27 is close to our estimate of 18 ✓ — but 1.827 or 182.7 would NOT be close, so we'd know to fix the decimal place.

✅ Answer: 6.3 × 2.9 = 18.27

⚠️ Common Mistake: Students sometimes put the decimal in the wrong spot and get 1.536 or 153.6. Estimation catches this — neither of those is close to 15!

✍️ Try It Yourself — Estimation

Estimate first, then find the exact answer:

3.9 × 2.1
Est ≈
Exact =

5.1 × 1.8
Est ≈
Exact =

0.75 × 4
Est ≈
Exact =

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📋 Quick-Reference Summary

Type	Example	Decimal Places	Answer
Decimal × Whole	2.4 × 3	1 + 0 = 1	7.2
Tenths × Tenths	0.6 × 0.3	1 + 1 = 2	0.18
Hundredths × Whole	0.15 × 6	2 + 0 = 2	0.90
Hundredths × Tenths	0.25 × 0.4	2 + 1 = 3	0.100
× 10 / 100 / 1,000	3.45 × 100	Move right 2	345

✅ Before You Move On — Self-Check

Ask yourself these questions:
☐ Can I multiply a decimal by a whole number?
☐ Can I multiply two decimals together?
☐ Do I know how to count decimal places?
☐ Can I use estimation to check my answer?
☐ Do I know the shortcut for multiplying by 10, 100, and 1,000?

🔓 Answer Key — Try-It Exercises

Page 2 — Decimal × Whole Number:
0.7 × 5 = 3.5 | 3.2 × 4 = 12.8 | 1.05 × 6 = 6.30 | 4.8 × 3 = 14.4 | 0.25 × 8 = 2.00 | 6.15 × 2 = 12.30

Page 3 — Decimal × Decimal:
0.4 × 0.5 = 0.20 | 1.3 × 2.1 = 2.73 | 0.12 × 5 = 0.60 | 0.7 × 0.9 = 0.63 | 2.5 × 1.4 = 3.50 | 0.35 × 0.2 = 0.070

Page 4 — Powers of 10:
2.7 × 10 = 27 | 0.45 × 100 = 45 | 1.306 × 1,000 = 1,306

Page 5 — Estimate & Exact:
3.9 × 2.1 ≈ 4 × 2 = 8, exact = 8.19 | 5.1 × 1.8 ≈ 5 × 2 = 10, exact = 9.18 | 0.75 × 4 ≈ 1 × 4 = 4, exact = 3.00

🚀 What's Next? Now that you understand the method, practice with the worksheets:

Open educational resources — learn, then practice!

📖 Tutorial: How to Multiply Decimals

📖 Tutorial: How to Multiply Decimals

📖 Tutorial: How to Multiply Decimals

📖 Tutorial: How to Multiply Decimals

📖 Tutorial: How to Multiply Decimals

📖 Tutorial: How to Multiply Decimals