Multiplying Decimals by Tens, Hundreds and Thousands

Learn to multiply decimals by 20, 30, 200, 600, 3000 and more: multiply by the single digit, then by 10, 100 or 1000. (For multiplying by 10, 100 or 1000 alone, see Multiplying Decimals by 10, 100 and 1000.)

1. The Decomposition Strategy

Key Idea:

Break down the multiplier into smaller parts. For example:

20 = 2 × 10
30 = 3 × 10
200 = 2 × 100
600 = 6 × 100
3000 = 3 × 1000

Remember: You can do the two multiplications in either order. Here we multiply by the single digit first, then by 10, 100 or 1000.

2. Multiplying by Tens (20, 30, 40...)

Example: 2.3 × 20

Think: 20 = 2 × 10

So: 2.3 × 20 = 2.3 × 2 × 10

Step 1:2.3 × 2 = 4.6

Step 2:4.6 × 10 = 46

2.3 × 20 = 46

2.3× 2 →4.6× 10 →46

Example: 3.12 × 30

Think: 30 = 3 × 10

So: 3.12 × 30 = 3.12 × 3 × 10

Step 1:3.12 × 3 = 9.36

Step 2:9.36 × 10 = 93.6

3.12 × 30 = 93.6

3. Multiplying by Hundreds (200, 300, 600...)

Example: 1.9 × 200

Think: 200 = 2 × 100

So: 1.9 × 200 = 1.9 × 2 × 100

Step 1:1.9 × 2 = 3.8

Step 2:3.8 × 100 = 380

1.9 × 200 = 380

Example: 4.15 × 600

Think: 600 = 6 × 100

So: 4.15 × 600 = 4.15 × 6 × 100

Step 1:4.15 × 6 = 24.9

Step 2:24.9 × 100 = 2490

4.15 × 600 = 2490

4. Multiplying by Thousands (3000, 5000...)

Example: 3000 × 5.7

Think: 3000 = 3 × 1000

So: 3000 × 5.7 = 1000 × 3 × 5.7

Step 1:3 × 5.7 = 17.1

Step 2:1000 × 17.1 = 17 100

3000 × 5.7 = 17 100

Example: 8.25 × 5000

Think: 5000 = 5 × 1000

So: 8.25 × 5000 = 8.25 × 5 × 1000

Step 1:8.25 × 5 = 41.25

Step 2:41.25 × 1000 = 41 250

8.25 × 5000 = 41 250

The Decomposition Method

Step 1: Break down the multiplier

20 = 2 × 10

30 = 3 × 10

200 = 2 × 100

600 = 6 × 100

3000 = 3 × 1000

5000 = 5 × 1000

Step 2: Multiply by the single digit first

Step 3: Then multiply by 10, 100, or 1000 (move the decimal point)

Practice Problems

Practice 1: Multiply by Tens

Calculate: 0.63 × 20

ShowHide solution

20 = 2 × 10

Step 1: 0.63 × 2 = 1.26

Step 2: 1.26 × 10 = 12.6

Practice 2: Multiply by Tens

Calculate: 5.1 × 40

ShowHide solution

40 = 4 × 10

Step 1: 5.1 × 4 = 20.4

Step 2: 20.4 × 10 = 204

Practice 3: Multiply by Hundreds

Calculate: 0.732 × 300

ShowHide solution

300 = 3 × 100

Step 1: 0.732 × 3 = 2.196

Step 2: 2.196 × 100 = 219.6

Practice 4: Multiply by Thousands

Calculate: 12.52 × 7000

ShowHide solution

7000 = 7 × 1000

Step 1: 12.52 × 7 = 87.64

Step 2: 87.64 × 1000 = 87 640

Key Takeaways

Break down the multiplier: 20 = 2 × 10, 300 = 3 × 100, etc.
Multiply by the single digit first, then by 10, 100, or 1000
You can multiply in any order - the answer is the same!
This method works for any number that is a single digit times 10, 100 or 1000, such as 30, 400 or 5000
Practice makes this method fast and easy!